The floor is slanted? You mean the ceiling, right? And no, I've never seen anything like that--except in a fun house.

This appears to be a ceiling problem. Is the ceiling really that far out of level, if so fixing that is going to be a challenge. Your contractor is right about needing to put the door in level, and cutting part of the door/jamb to make it follow the ceiling is going to make it worse than it is right now. The solution to this is either fixing the ceiling/floor above this area(requires removing the ceiling and looking at the joist), or bringing the sheetrock on the ceiling down to match lower part of the ceiling (would require adding shims or more sheetrock and a lot of sheetrock mud to make it look flat. If it was my house I would want to know why that ceiling is so far out of level as it may be a structural issue with the floor/s above it. In the second picture it appears that the double doors and beam supported by the post are level along with most of the ceiling. did you have a cracked basement wall or extensive settling in the corner by that door?

Since "there's nothing he can do," ask him if he can recommend a good contractor. ;)

As d michael described, the ceiling not the door is the problem, no carpenter tricks can make that look any better without addressing the ceiling,

Thank you for your quick feedback! I'm waiting for my husband to give me the correct answers to your questions.
What I can say for sure is this entire ceiling is newly finished by THIS contractor, so when he laid the floors built the walls, doors, and closed up the ceiling, shouldn't he have compensated for the unevenness??

I attached a picture of the entire door (the white steel door leads out to our garage), as well as what's inside the closet, as it may provide insight that I'm unaware

I appreciate all your feedback!! Thank you!

I'd take this approach:

1) if he built the ceiling, floor, and walls, then anything out of level/plumb is on him, so he has to make it right. get out your level and verify for yourself what is going on. then be prepared to work hard to get things done right.

2) however the fight in #1 goes, I'd paint the door frame(s) to match the walls, and then paint the doors a contrasting color. once things are painted, the frames disappear and you'll only notice the door, which is fine.

Most sheetrock hangers do not check for level on the ceilings, even though that is the easiest way to fix the problem. as far as adjusting the floor, it would not have helped the fact that the door stays open or closed lets me know that it is pretty close to level and the reveal or space at the bottom of the door seems to be even which is why i think its a ceiling problem. Should the contractor have checked to make sure the ceiling joist were level, probably, but 90% won't. The only issues I would have with the contractor at this point are (1) why was it not brought up as soon as the sheetrock went up or at least when the door went in. (2) there is nothing that can not be corrected so saying that there is nothing he can do is a lie. it can be fixed but more than likely it will be a change order costing you more time and money. if he brought it up as soon as the sheetrock was hung it would have been easier/cheaper to fix and would not require extra trim, paint and time.

Oysters! What have we here?! Is that a rusted section of cast iron pipe? Is that moisture causing that pattern on the spray foamed (?) wall? Is that an open sump pit?

I gotta ask (no judgment, btw!): Was this job permitted and inspected?

Acm - that's been my design plan all along! The walls and trim will be painted the same shade of white and the doors will be blackish

Sammy - I wish I knew the answers to those questions...waiting from my other half for the more technical info...what I do know is 1) that pipe was behind an accordion partition inside a smaller closet when we purchased the house and 2) the spray insulation was done about a month ago

D Michael - I agree with you. And our contractor is a decent guy who has been great to work with. He's "trying to figure something out" -
It's tremendously helpful hearing objective feedback from professionals like yourself

Thanks again to everyone for taking the time to reply!

Michelle how did your contractor do that? Is it a wood door?

yes he did. The floors are not wood. They are called luxury vinyl. It was a perfect fit for a basement. Looks just like wood

Michelle Is the door Sheetrock? Wood slab? Is it magnetic open/close?