It's a bit harsh to say they are a social embarrassment. I think some people do like to play it up though because it's become somewhat of a trend to be "socially awkward" nowadays, even though there are also lots of other people out there who do get nervous and shy and it's completely normal (not trying to belittle people who have anxiety as I unfortunately have had to suffer with that badly in the past but, even now I'm still shy). But some people do just generally get tired out after social interaction, and do generally prefer listening over talking in conversations. However, you can still be good at socialising and also be an introvert. I'd say I do get pretty nervous when being around large groups of people but, even so, I'm still a friendly person. If someone talks to me I'll talk to them too, I try to seem approachable to others and even though I will admit that by the end of the day I do feel worn out, it isn't because I'm a social embarrassment. And that's probably the case for the large majority of introverts - we are able to go out and enjoy ourselves and hang out with friends and talk to people, it's just unfortunately is draining for us, and we value alone time much more perhaps than an extrovert would do. I always have to have a bit of alone time at the end of the day to just relax and unwind and think to myself just because I'm an introvert.
So really, I do agree with you, it is a bit irritating and unfortunately embarrassing when people try to play up being an introvert and being "socially awkward", making it seem like it's a cool and trendy thing to be, when it's not really. It's not fun to be like that. But I think it is again harsh to say that people are social embarrassments because they are introverts, as the vast majority of introverts actually can socialise and talk to other people, it's just they find it draining.
Edit: Oh whoops, my bad, I misread what you said! ^^" But my point still stands anyway since I know a lot of people who say similar things like that about introverted people.... (welp, I've had people say it to me too)