Somewhere on the site, you posted something that the other person can relate to. A joke, a common denominator,etc. Maybe the WAY something was said. I usually always accept friend request but recently I've become leary of brand new members.
Chess.com Friends
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friends 
if i like someone i friend request them so i can find them in future and talk to them
most of my friends are people i like a lot or been talking them i add them to friends see i can talk to them more in future or people who like me and friend requested me
i dont keep anything secret on my page so everone can see everthing on my page so friend or not you can read everthing but friends i talk to most of my time and go out of my way for
i dont know if everone can see everthing i say? inside clubs
i think you have to be inside club to be able to read everthing
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Sure I do not mind "friends" on chess.com, but my primary focus is to improve at Chess (to more competitively play against my friends in person OTB). However, this got me thinking - Philosophically, why do people send chess.com "friend requests" to each other? Of course, (as with any site) a "friend" is a very superficial relationship - but a type of friendship, regardless. In the case of chess.com a "friend" gets easier access to their profile via your own profile; basically, this enables easier access to track "friends" rating, forum posts, stats etc. I believe that the following are some of the reasons to get chess.com "friends":
1) You know them personally, so chess.com "friend" is really just a reflection upon their "friendship" in person.
2) You just like to interact with people and perhaps try to accumulate "friends" as with many other sites online.
3) Upon viewing their "profile" (or perhaps even communicating via "messages"), both people share several thoughts/ideals prompting you to send a "friend request."
4) They responded to a forum that you created (or they posted in a forum that you read) and you sent a "friend request" as a result. More likely, after viewing their profile (either by interest or reciprocity).
5) You are a newer chess.com member and the other person helped you in some way (even if they do not know it), so you sent a request.
6) The chess rating of the opponent was favorable for you. Usually this means that the ratings were somewhat close to yours, but sometimes the fact that they are much better Chess players serves as the actual reason for your interest - typically with the thought that you will learn from them, either by advice or by playing Chess games against them.
7) Perhaps you enjoyed playing a game against them - and this sparked interest into them as more than just an opponent for one game. Maybe you just liked their play style/ability at one game aspect, or maybe the game was enjoyable for another reason (like you both agreed to draw in a past game).
8) The picture - as silly as it sounds, the avatar that they use on chess.com is important. Of course, the person in the photo may not even be them - but it certainly says a lot about them. Furthermore, this is the only visual that you have to your chess.com opponent. Often times the "halo effect" could be applied into a chess.com "friendship" via the avatar they use. Perhaps the avatar is of a character you like arousing happy memories (like an avatar of a childhood tv character you liked), perhaps it accurately reflects the chosen username, perhaps you just like the picture (for this one, probably a landscape or drawing).
9) In the same grain as number 8, the username can influence how you view them. Some usernames on chess.com are really funny, some reflect the avatar well, some are just clever - and any of these causes you to investigate them further (like viewing the "profile"), or simply to send a "friend request."
10) They are in a chess.com club that you are a part of and this prompted you to look into that person.
A lot of these are similar in nature, but there may be many other reasons to acquire chess.com "friends"; the purpose of this forum is to say why you became a chess.com "friend" to someone, or suggest some reasons that I did not list (in the list of ten above).
Personally, I like to know a little about them (either in person or via "profile") - but sometimes I have simply accepted a "friend" request simply because they sent one to me (and who am I to refuse? I don't want to be rude, maybe they have a reason). In short, why have chess.com "friends"? I am curious to hear some responses
I know you must be dedicated - you read this really long post 
Okay perhaps you were just bored/had time, but I am still eager to hear why you accept the friendships you have on chess.com