So to give a little bit of context, I just graduated with a Bachelor's degree this past Friday. At my graduation ceremony, my best guy friend attended and met my parents and family after the ceremony. My friend couldn't visit for very long as he had to be at work soon after, so we just got a few pictures together, introduced him and hugged and said goodbye. Now I guess you could say him and I were a little affectionate with each other as we hugged probably about 3 or 4 times in that interaction. We hug each other regularly, sometimes exchange "I love yous" etc. Overall him and I care very much for each other. Because of this, mom doesn't seem to think our friendship is purely platonic. I know for a fact he doesn't see me that way and neither do I towards him. Do you all have friend(s) of the opposite sex that is purely platonic? What is your friendship like? Do you show any type of affection towards each other? In general, are men and women capable of being just friends?

There's a difference between being friends, being close friends, and being REALLY REALLY close friends. At each stage the likelyhood of a relationship increases substantially. At the end of the day it depends on you two, how 'affectionate' you are with each other and whether you remain the same or keep getting closer and more affectionate. You may be platonic now and not be in the future, or you may still be platonic in the future. It is possible to just be friends, but increasing amounts of physical affection does make that less likely.
A side note, never say you know for a fact how someone else feels about you. You don't. Lying is very easy and people tend to not be honest about their feelings towards those they like. I'm not saying he likes you, just that you should never assume 100% certainty.

It is possible. My best friend for a decade has been a guy. We both attended each others weddings and he had even been our roommate for 8 years.

Yes.
I'm not even bothered to explain bc once someone thinks it's not possible for friendship to exist between different sexes, they not gonna change their minds.
Just let your mother be.
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If what she believes is true, I'd not be able to befriend anyone as I'm half gay.

ive seen people try to mix this stupid idea with the stupid idea that all women are bi into some stupid "proof" that the stereotype of all women constantly backstabbing and hating each other to be true

Yeah I have plenty of female friends that I'm very affectionate with that I've never been attracted to

I have plenty of female friends I have no interest in, and we have been friends for anywhere from 2-9+ years, and none have made move towards me or vice versa. I find it easy.

I have been with friends with woman a long time ago, so to answer your question, yes, the opposite sex can be friends with you, now if your parents are not keen on you having friends with the other sex, try and reason with them, give examples that in ways you can be friends with the other gender, i hope this message helps, peace out

Most of my friends are girls soooooo

I don't think they have an issue with me having friends of the opposite sex (also I am an adult and I get to choose who to be friends with anyway) but she has asked me on multiple occasions, even before they met him, "And you're sure you are just friends?" Because I talk about him a lot to them because we are so close. My friend and I have also had a conversation previously about romantic feelings and we just have a mutual love for the other that isn't romantic. I guess I'm just annoyed that mom keeps asking about us just being friends and I don't want her to expect that more will come out of it because it won't.

No matter your sexuality, you end up attracted to specific people, not to an entire gender. So it's totally normal to be "just friends" with many people of your preferred gender. But the phrase "just friends" is stupid because it implies that romantic love is the ultimate goal and is somehow above platonic love, even when the two can be equally strong.

Just because you are able to be friends with members of the opposite doesn't mean that others are capable of the same thing. I am often accused of sleeping with male friends even though we've never had sex together. I just feel bad for those who are unable to have friends of the opposite sex. They're missing out on so much.

@laughwendylaugh Entire perspectives and experiences, yeah. I’d rather not miss out on it. I understand my fiancée better /because/ of my deep friendships with women.

Of course. I have many guy friends. Who are just friends and nothing more.