A first date is really just to see if people are compatible. It isn't any one persons responsibility to foot the bill unless they were perhaps insistent on a specific place or activity. That being said its a classy move to offer to pay, if you can afford it and really want to make a good first impression.
Long story short just don't insist that the other person pays and you will be fine people.
Long story short just don't insist that the other person pays and you will be fine people.