I just read about that on his page here and was surprised. MM3 is my second favorite Mega Man. I wonder what he had in mind for the game. I'm betting he wanted players to see more of Protoman's story.

As written in the wiki, he told Nintendo Power it was rushed out before he thought it was ready. Here's the actual quote:

Inafune explained the reason why is because of "...what went into the game and what was behind the release of the game." He also stated that he was forced to put the game out before he thought it was ready and during the game's production, the developers lost the main planner, so Inafune had to take over that job for completing the game. Inafune concluded, "I knew that if we had more time to polish it, we could do a lot of things better, make it a better game, but the company (Capcom) said that we needed to release it. The whole environment behind what went into the production of the game is what I least favored. Numbers one and two - I really wanted to make the games; I was so excited about them. Number three - it just turned very different."

"As written in the wiki, he told Nintendo Power it was rushed out before he thought it was ready. Here's the actual quote:

Inafune explained the reason why is because of "...what went into the game and what was behind the release of the game." He also stated that he was forced to put the game out before he thought it was ready and during the game's production, the developers lost the main planner, so Inafune had to take over that job for completing the game. Inafune concluded, "I knew that if we had more time to polish it, we could do a lot of things better, make it a better game, but the company (Capcom) said that we needed to release it. The whole environment behind what went into the production of the game is what I least favored. Numbers one and two - I really wanted to make the games; I was so excited about them. Number three - it just turned very different."

"

I don't know how you can improve on Mega Man 3.  It seems pretty much perfect for the most part.

*shakes Dalai's hand* Yeah in Mega Man 3 you got to fight my favorite MM character, Protoman, many times. MM3 is not that far from Mega Man's 2 greatness at all. I'm still guessing that Inafune wanted players to see Protoman's story before the game (which I just readn and LOVED) and his story during the game. I only had a clue about Protoman's storyline after his ending in either Mega Man: Power Battle or the sequel Mega Man Power Fighters (I can't remember which game it was since I got both on the same disc. And that was not much at all. I just really learned about it from the Protoman story that giantbomb has posted:

 

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