Why Saitama doesn't want to unleash his full power? So far my impression of Saitama is him holding back his power.

Even when the "Strongest" Alien in the universe attacked him, he easily finished him with NORMAL punches. He hasn't unleash his full power and I'd like to know why.
Saitama wants to find an opponent worthy of his power. 

He commonly fights enemies, killing them with one-punch, hence the name. He has found that launching a full punch kills almost everything he face. There's no challenge in that.

So yes, he is pulling his punches. There will be multiple times where he can easily destroy his opponent, but does not "try" until it has shown to be strong enough. 

He is a hero for fun. Not to save people, but to enjoy the thrill and be himself. 

I've avoided spoilers the best I can, especially since I'm not sure how far you are.