Sorry, this is really long, but I thought you'd want my entire explanation.
It's popular notion that heterosexual men and women cannot have a platonic friendship because sex gets in the way, and they certainly cannot be best friends. This, my young children, is a lie.
Why People Believe It:
Reason #1: That's the way it was back then, it's the same way now.
Counterargument: Looking back in humanity's past, women and men have been separated from each other and had contact limited to marriage and making babies. They were never given that chance to connect. Now, however, we are raised together, and have interactions with both women and men on a daily basis.
Reason #2: We don't have enough in common.
Counterargument: This draws upon a number of sexist social stigma that are reinforced from childhood. Men are taught that women are less than them, that the only thing they should care about in women is their beauty and their use to men, and that it is important to be dominant.
On another side of the gender spectrum, women are taught that they are supposed to be submissive to men and that they should look and dress in such a way that prizes a flawed, ridiculously unattainable appearance, and that they must limit themselves from "manly" activities simply because they are women.
We are taught from birth far too many negative things: women can cry and have emotions like real people, but men can't because "it's not manly". Men can be treated like real people and women can be objectified. Women who are sexually promiscuous are whores, but men are heroes if they have lots of sex. If women are virgins, they are holy magical creatures to be worshipped, but if men are virgins, they're losers. Both women and men are told that men are nasty, disgusting beings that only care about sex, while men and women are told that women are annoying, shrill things that only care about their appearance.If you agreed with any of those sentences about male and female stereotypes, I suggest you alter your worldview and take a step back to think about how much you and others are influenced by the media, and what the media is telling you to be.
The truth is, women and men really do have a lot in common. We just can't trust stereotypes, because everyone is different, and we can't trust the media because it will lie to us and tell us what we can and can't be. You can be whatever you want.
Reason #3: Sexual attraction ruins any commonalities.
Counterargument: Just because you find someone attractive doesn't mean that means you immediately can't be friends. Acknowledge it, and then move on. Don't demean the worth of friendship with someone because you're interested in them--the worth of a friend is just as much, if not more, than the worth of a romantic or sexual relationship. One friend doesn't have to be a homosexual or Sheldon Cooper to be friends with someone of the opposite sex. All that stuff your family and friends tease you about when you hang out with someone who is not your gender, or things that you say, like "Oh, is that your girlfriend?", "Are you two dating? Because you're always together", or "They're all over each other, it's obvious they're having sex", you need to stop. There is no point in separating the male and female genders.
Reason #4: Guys are only in friendships with girls to get into their pants.
Counterargument: First of all, that's sexist. Like I said before, not all men are the same. Sometimes (and this is a real shocker, I know), people are just nice because they're nice people. There are people who want to be friends for no other reason than because they want to be friends. Simple as that.
Second of all, for those of the people that do, you can't automatically assume that all men are douchebags who pull the whole "nice guys finish last" thing. It's not uncommon for men to know that women are not tools or machines, and you can't just throw women a cookie and expect them to have sex with you. Women are, always have been, and continue to be, human and must always be treated as such.
(By the way, "friendzoning" is overamplified and "relationshipzoning" is underamplified. People who are into dudes don't go looking specifically for assholes that will treat them badly, they look for people who have the confidence in themselves to go for it. They don't go for guys who play the "nice guy" card and pretend they're angels and that women are blind. Just because you're there for someone doesn't mean you need to hook up. Your best friends are probably always there for you, but that definitely doesn't mean that now you have to have sex with each other, right? It's not okay to think that just because you're nice to a person doesn't mean they must now let you screw them. People are not pretty trophies that you work for.)
So yes, men and women can be friends. Best friends, even, to answer your question. It's not just some magical occurrence that only happens in fairytales and stories. It's real. I assume many of you think that it's not okay to exclude a person from being your friend because of their race, religion, or sexual preference. Why is gender any different?
But you had a very good question, and a very reasonable one. I hope I answered it.