Why do men always want to pay for our stuff?

Many reasons, one of which you have literally opened with - there ARE women who want men to pay for their stuff.  You even say that it's ok on a first date, so on some level, you even accept it, yourself.

Other reasons:

1. Being brought up that way.  It's possible that their parent/s have instilled in them a sense of chivalry that a woman is a prize to be earned, and once you "win", not to forget what a prize they are and to treat them as such.  In recent years there has been a fair bit of pushback to this idea which is a whole new rabbit hole I am not going into, but the point is that it could be how they have been raised literally from birth.

2. Sexism - yes, it CAN be a reason, but it doesn't necessarily have to be the only explanation.

3. Some women have been raised/have rebelled against their upbringing and believe men should pay for everything (literally seen a question on here in the past week asking if it was OK for her to believe that a man should pay for everything, her rent/bills, give her an allowance and take her on holidays.  What does the guy get in return?  "Well, he gets the girl, isn't that enough?"  No I am not kidding, this was a real question on here).

4. Some women say they don't want men to do this, but this turns out to be a test and said men are then socially destroyed for being "cheap" or "not knowing how much of a prize I am".

So you don't like it anywhere beyond a first date.  Fair enough.  That is a preference you have.  You have a right to that, but you also have to communicate that to men you date.  Do not expect them to just KNOW this, as all women are different.  Maybe he has previously dated a woman either who genuinely believed the guy should pay, or one who put him through the sh*t-test option.  You should tell him that you are not sh*t-testing him and that if you are going on more than just one date with him, he should feel comfortable bringing up the topic of paying so you can discuss it between you.

It's how they've been brought up and for some it been so drilled into them from an early age that it simply feels wrong to let a woman pay for her own stuff. 

I get where you're coming from, though. I grew up with high gender equality and where it's normal to take turns paying or going Dutch, and I until I met my husband, I never went out with a guy who had any problems with this.

My husband on the other hand is the kind of guy who'll open the door for a woman, tell her to wait while he runs through the pouring rain to get the car, pulls out the chair for her to sit, helps her on with her coat, and yes, pays for the meal. He was respectful and grudgingly allowed me to pay for our second date, but he was so visibly uncomfortable (I swear, I could see cold-sweat trickling down his brow) with it that I honestly didn't insist on it again. It didn't sit right with me having him pay for everything, though, so I'd even out the score with home-cooked meals, gifts etc.

It is an old gender role some men still adhere to. Some women enjoy being provided for but others want to make their own money. 

If I'm inviting someone I usually like to pay for that reason...you don't make guests usually pay for their food when they're visiting. But I don't mind sharing the bill otherwise...

cause they think its a nice thing to do