The motivation issue is a big one. If he isn't highly motivated and is content with a low level laborer job-- and that is not acceptable to you, then you need to recognize that he is not going to change this aspect of his personality.
It seems to me the big issue is the lack of motivation, and the handy-man stuff is just sort of a tacked on slam to add to the negative column...
But the handyman thing I take a different view on. I think that two adults in a relationship need to work from your strengths. If doing handyman stuff isn't his strength, then don't feel like you are getting "less of a man" because he doesn't want to or like doing that stuff. Many women today DO like doing it and are good at it when their spouses aren't. The idea of a marriage is that you work together and pool your strengths to counter your weaknesses. Not that every man has to be able to do x, y, z and every woman has to be excellent at t,u, v.
How would you feel if your husband let it slip that he wasn't sure he could be married to a woman who wasn't a good seamstress and didn't make clothes for him to wear, and the drapes for the bedroom, and the bedspreads. Would you be on board with that type of thinking? He doesn't want to buy pre-made clothing, he wants his wife to make it. Wives do that.
Yeah... doesn't feel so good when you look at it that way, does it? Same thing. If sewing is something you are good at, then you might not mind making a table runner or a pillow cover or whatever. But I'm betting that you would be ticked if your spouse expected you to be able to sew EVERYTHING that needed sewn.
There are plenty of areas of around the house stuff that each of you may excel or be weaker. Repairing plumbing or hanging ceiling fans are just one aspect. There is keeping up a lawn (mowing, edging, mulching, fertilizing, treating for bugs, and choosing and planting landscape plants, not to mention irrigation), taking care of cars (oil changes, tire rotation, regular other maintenance), taking care of bills (balancing checkbook, online bill paying, deposits, due dates, rates on loans, etc), cooking (menu planning, grocery shopping, cleaning up after, budgeting), and so on. Tons and Tons of things that you might be better suited to do. Some of it he might be better suited to do. You will not BOTH be suited to everything. Just won't happen.
My own husband isn't as gifted in the home repair department (very minor things, fine. But anything involving water or electricity rates a call from a licensed professional). But he does the lawn. And he put enough effort into his education/career that we can afford to pay for the occasional licensed professional for the things that require it. But, I take care of the pool, and the stuck disposal, and changing the a/c filters. We can both change light bulbs, but he does the ones that require a ladder. :)
The household stuff is only an issue if you don't both take on what you are good at. Unless you are suggesting that he has ZERO ability to do ANYTHING around the house. And you didn't say that, you said he helps with the laundry and the dishes. So, let that become his domain, and you take on something else. What neither of you are talented at, you hire out, or get a copy of " ____ for Dummies". Those are not marriage breakers.
General laziness and lack of motivation... that you cannot ignore.