ESH

Your girlfriend's sister is just playing a fool and goading the your sister. She very clearly isn't trying to set your GF up with this guy, she's just doing what sister's do. You could say, however, that she may be pushing it a bit much, since this older man does seem rather invested in trying to woo your girlfriend.

You angrily flipping out on her sister was out of line. Your girlfriend is her own person, she has the ability to stand up for herself if she does feel uncomfortable and it is not your job to stand up for her towards her sister, as it sounds like they have a sisterly relationship and are just goofing off.

Obviously this older man is in the wrong, both for being outright weird and for flirting with a girl that he knows has a boyfriend. However, these things happen, and it isn't worth upsetting your girlfriend' sister over.

You are being protective of your girlfriend, which us perfectly fine, but you were out of line to get angry at your girlfriend's sister. Your girlfriend's sister is just fooling around, and it is pretty clear that your girlfriend has no intention of getting with this older man, as she is with you.

If you are concerned that he is going to do something dangerous to her, talk to your girlfriend about and express your concern. Otherwise, apologize to your girlfriend's sister and realize that sometimes people are weird and are going to have a fancy for your girlfriend, it doesn't mean you need to be hostile about it every single time.