Husband thinks I should do all of the housework and childcare?

So my husband is being a sexist pig, in my eyes. He works full time, 10 hours a day, 6 days a week. I work part time, 6 hours a day, 4 days a week. I also primarily take care of our daughter who is 3 years old. My husband expects me to cook every night, do laundry, dishes, clean the whole house, and take care of our daughter alone. The only thing he expects to do is go to work. I’m so mad about this that I’ve written out a general list of what the hours look like in our week. This is a typical week.

The reason his sleep estimate looks the way it does is because he often stays up playing video games with his brother at night, or working out later. He has Sundays off from work.

I have tried to make a chores list, giving myself more chores than my husband, but keeping it fairly even where I can.

This is not good enough for Husband. He says that he shouldn’t have to do any housework, because I’m a woman and I work less than he does. He won’t even pick up after himself, leaving a trail of messes wherever he goes and expecting me to clean it up. Let me also add that my job covers the cost of tuition based preschool for our daughter. She would otherwise be staying home everyday, starting Prek next year when she is 4 years old. If I didn’t work, we wouldn’t be able to afford to send her to Prek this year. My husbands paychecks barely cover the cost of living per month that we have, and more often then not, the little extra $100-$200 I have left over after paying for school helps us to get by until he gets paid again. How do I convince my husband that he needs to help out around the house? I feel like he wants a housemaid, not a wife.