Here's my best argument: 
 
Once you are finally done with the game, you can understand why people stick their penis in the disc holes.

The problem with the Half-Life story that some people have is that they "show" you the story rather than "tell" you the story.  It's a classic film technique, but it's relatively new to games.  The designers present  you a scene, and you're left to your own devices to figure out what happened, just like real life.  To find out anything about the 7-minute war, or whatever, you have to wander over to some newspapers posted on a wall, and an NPC will make brief mention of it for you.  Explanations aren't given for a character's missing legs, or the switching sides of the Vortigaunts,or the motivations of G-Man but enough clues are given that you can fill in the blanks yourself.  You know as much as Gordon Freeman does.  I hope they start filling the blanks in a bit more in the future, but it's defiintely an interesting take on game stories, one you'll be somewhat familiar with if you've paid any attention to Left 4 Dead's plot.  If your response to that is "what plot", then Half-Life probably isn't for you.
 
And you will miss out significantly story-wise if you haven't played the first.

" First off, Black Mesa was a facility that accidentally opened up a portal to another realm, releasing an utter shit storm upon the complex.  While all the scientists were being killed off by headcrabs and armed military goons, Freeman took up a crowbar and fought his way out, and leaving a trail that presumably allowed others to get out in his footsteps.  This, mixed with his ending the enslavement of the Vortigaunt and his capacity to overcome impossible odds are why he's seen as such an epic hero.  Also, the reason characters keep saying they're from Black Mesa is because even someone that played HL1 wouldn't necessarily know they were from Black Mesa.  There were no unique characters in HL1, instead having a bunch of generic scientist and guards running around.  However, the main characters of HL2 have appearances that are a tossup to the generic skins from HL1.  The characters, now having unique identities, are simply confirming that they were one of those insignificant individuals you encountered at Black Mesa.
 
As far as HL2's story, it's presented through the eyes of Gordon as he experiences it.  There is no narrator telling you the plot details that the common man would have no idea about.  This is meant to immerse the player further, I suppose.  The storyline is mankind's epic struggle against this new fascist, alien regime that is slowly walking us into extinction, and you're seeing just one perspective in all of that.  And since that perspective is from the man that everyone looks to to lead the revolution against that regime, the story is told primarily through you taking the fight to the Combine.  
 
The game does pick up as it goes on.  But not so significantly that I would guarantee you'll enjoy it.  I love the game in its entirety, but it is starting to get dated.  That sense of innovation that made the game so amazing is going to slowly disappear as time goes on.  For someone like me, every time I play it I'll be able to appreciate how awesome it was the first time I tried it out.  But, unfortunately for those that were late to the party, they'll never get to experience that.  However, I recommend you at least play for a couple more chapters.  The physics engine, which was a large part of the innovation that made the game so crisp, isn't fully utilized until you have the gravity gun.  I hope you're able to enjoy the game and see it through to the end, because it is a fantastic game.
 
Edit: 
@ The various posters the feel there is not a storyline: The storyline requires the player to be observant to the state of their environment to realize what's going on.  Examples of this would be the portions of the game where you find docks sitting out over what appears to be desert, with an occasional abandoned boat laying in said desert.  At some point I think the developers expected you to realize, "Hey, this isn't a desert.  This is what used to be the ocean floor.  Those Combine s'umbitches are takin' our water!"   There is no formal exposition.  This is true.  However, by throwing the player into a setting drastically different from the first game, the developers seem to have intended to spark the curiosity of newcomers and those that completed Half Life 1 alike.  However, while this was effective for the latter group, it backfired for newcomers, who erroneously assumed that this new setting was explained in HL1. "

I actually uninstalled it a couple of months back.

" @TooWalrus: I was the exact same, I never finished it. "

The fan boat ride goes on for a bit too long, I think you should play past that and at least to Ravenholm before dropping it if you're not digging it. 

We Don't Go To Ravenholm!

Later in the game, you lead a bunch of bugs in an assault on a prison. 

It's an amazing game! That should be reason enough^^ 

" So he lent me the Orange Box, and after spending several hours on the first 5 chapters, I took the disc out went to play something else. There literally wasn’t a moment in those first 5 chapters I enjoyed."

You shouldn't.  Case closed.  HL2 is just not fun for sane people, is all.  Just ask Jeff.

The last 1-2 hours of HL2 is what makes the game actually good, so if you've already invested a significant amount of time in it, you may as well experience the ending which redeems the rest of the otherwise shoddy game. 

I've never been able to convince someone to play this game, all the parts that they / you didn't like I loved. I literally can't think of anything else to sell it to someone when the only barrier is that I like this kinda stuff and they don't.

Dilemma.

" You shouldn't.  Case closed.  HL2 is just not fun for sane people, is all.  Just ask Jeff. "

I've yet to see anyone mention how they "loved" the parts where you have to fight the airship assholes, or the tripods, or navigate that trip mine room, or walk on the struts of the bridge.... Yeah, fun right? NO!

If you need to ask people to convince you to finish a game, you shouldn't finish it. Half-Life 2 was groundbreaking in many ways, but parts of it were very poor by 2004's standards, and are even worse today's standards. For example, the pacing in that game is pretty terrible. The game definitely isn't for everyone, and if you're not enjoying it, just stop playing it.

" I've yet to see anyone mention how they "loved" the parts where you have to fight the airship assholes, or the tripods, or navigate that trip mine room, or walk on the struts of the bridge.... Yeah, fun right? NO! "

Fuck HL2. 

Go play the first Half-Life, its better in every way.

It's one of the greatest games of all time. If you're not enjoying it, then don't play it. Just know that your opinion is wrong. 
 
(lol)

" It's one of the greatest games of all time. If you're not enjoying it, then don't play it. Just know that your opinion is wrong.  (lol) "

I played it shortly after it came out and wasn't that impressed even at the time. This is nowhere near the best FPS ever, really. 
The physics stuff was nice back then, the end is kinda cool and I didn't mind the vehicle stuff, but yeah, it's basically 1984 - the game.
I still love HL1 though. THAT was amazing when it came out.
And god how pukingly amazing and fast was HLDM?
 
I'm old.

It is probably my favorite game of all time. Why? Because everything it does/is appeals to me. If that doesn't appeal to you and you don't enjoy it, don't play it. Reverberated opinions do not equal empirical truth.

The game is amazing on the PC but it's total shit on a console.