I don't agree with the constant badgering that your parents are engaged in. But I think you and I should have a little thought exercise to try and see the situation from their perspective.
For whatever reason, your parents are worried about you. They don't think you're happy, and so want to motivate you to do things that they think will make you happy. They're not doing this to be mean, or because they hate you. They just think that, because you're 24 years old, you should be going out and meeting people and doing things that they consider fun.
You shouldn't lie to them. And you shouldn't shut them out, even though they are making you feel bad. Your best bet is to just talk to them openly about your life. Tell them that you enjoy staying home, that you do indeed have friends, and that you have a happy and healthy life.
You may never truly convince your parents that your homebody-ness is a good thing, but if you're honest with them about it enough times, perhaps they'll stop pestering you. It's your life to live, and so long as you are enjoying it, you're doing it right.
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I could be wrong but I'm picking up from the letter that the guy is probably depressed and not totally happy. He said he's "content" - I went thru a period like that. I was so depressed and socially isolated that going out (like to bar or a party) felt like more pressure than a chemistry final exam and I would avoid all situations like that. I actually did lie to my parents telling them things like i was going out to dinner with a friend, or going to such and such event when I was staying home. Now, I did eventually get help and started feeling better and no longer have that problem.
I would suggest being honest with your parents and by that i mean honest to the point where if you don't go out because it feels like too much tell them that. Ask them to help you find/think of situations that would be less scary for you. Maybe that involves going out to dinner with a friend (or with them) or going to a movie (doesn't require much talking or social skills). Sometimes what you need is a friend to go with you to new events, maybe your mom or dad could be that friend if you don't have anyone else? Not saying you should hang out with your parents forever but until you can make a few new friends and get out on your own.
You could also try meetup groups - there are lots of ones with pretty specific interests and that might help you branch out and meet new people. It doesn't have to be all bars/clubs/parties - maybe you'd prefer to meet up with people and play video games but I think the key is getting out there and hanging out with other people more often. It does a body good!