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Guys, would you be cool with it if your girlfriend hung out with her male best friend who isn’t gay?

Ladies, would you be cool with it if your boyfriend hung out with his female best friend who isn’t lesbian?

I’m having a girlfriend for the first time at 32, she’s 42. Due to the fact that she’s my first girlfriend I’m very immature and naive. I think like a 12 year old in terms of romance. I don't know if the good outweighs the bad. So in this question I’m gonna share with you the pro and cons.

Pros
1. Food: always cook for me on her days off. Even took the time to learn my favourite recipes.

2. Budgeting: She’s very smart with her money. We both have over 50k saved up with no debt. We have it planned to buy a house together and pay a low interest rate.

3. Open-minded: I can talker her about almost anything and she’s a good listener.

4. Very sharing: She let me borrow her car for 3 weeks when mine got totalled. Every time she gets bonus pay she’s willing to spend on me.

Cons

1. Has temper: Every time she has to explain something to me a second time she screams me. We end up fighting and not talking for days.

2. Conceited: She believes she so hot that every man in the world wants her. Her exact words “I have a big ass and D cup breasts. Every guy wants me”. Women should be confident but this is ridiculous.

3. Verbal/Emotional abuse: She tells me that I’ve never had a girlfriend because I’m socially awkward & weird. And how I’ll never find anyone better than her. And that the only reason she agreed to date me is because I’m handsome with muscles. And if I stop working out she’ll replace me.

4. Shallow: She refuses to date guys her age and only wants younger men. Nothing wrong with dating younger, but refusing to date your own age is dumb.

5. Male friends: She only has 4 female friends, the rest are guys. She even admitted a couple of them want her. She has a male bestie Alex who she texts almost every day. Whenever Alex has a girlfriend he barely texts her and she gets mad. She agreed not to hang out with guy after I told I’m uncomfortable, she said I’m “just being jealous”.

Is this how a relationship is supposed to be? please give me the best advice with your comments.