Let's try another example. Imagine someone considers themselves a proud makeup wearer. People would think that's pretty silly too - people wear makeup, they enjoy it, and might even consider it a necessity to be accepted by other people, but nobody would say they're proud of it (gay pride aside if you're in an area where being male and wearing makeup automatically means you're gay).
Gaming is a similar thing, you can play games, enjoy them, possibly even play games because it's a common social factor, but to say you're proud of it, that gets a bit silly. You're making gaming a central aspect of your life that way, and for the most part gaming is recreational rather than productive.
Now as for people looking down on someone just for saying they're a gamer (with no mention of proud), that's pretty silly too.
Gaming is a similar thing, you can play games, enjoy them, possibly even play games because it's a common social factor, but to say you're proud of it, that gets a bit silly. You're making gaming a central aspect of your life that way, and for the most part gaming is recreational rather than productive.
Now as for people looking down on someone just for saying they're a gamer (with no mention of proud), that's pretty silly too.