Your parents are definitely right.

Context matters a lot, which means you need to put yourself out there in the right context to meet someone. Examples: trivia night at the local bar, or a book club, or a local live music show. Most women aren't gonna be interested if you approach them while they're just living their lives grocery shopping or at the gym* or something - that's not a social context. (*Unless you're regulars at the gym and run into each other and chitchat all the time, but I'm assuming you're not in that kind of situation.)

Once you're in the right context, and you see a woman you're interested in, start by very casually talking to her, and keep an eye out for signs of interest (e.g., turning in their seat toward you which indicates they're giving the conversation real attention, or moving the conversation forward by making jokes or asking follow-up questions) or disinterest (e.g., one word answers with no follow-up engagement, turning their body away from you, mentioning a boyfriend). If you see signs of disinterest, just stop and let her be. But if you see signs of interest, continue the conversation. Don't be too needy, don't come on too strong, let the conversation breathe. And for godsake don't buy her drinks, it's cheesy and puts too much pressure on a new situation. Especially don't buy her a drink without even asking her first, it's pushy and I can't speak for all women, but I fucking hate that. Ask her about herself, for example her interests. Try to get a gauge on whether you're attracted to her on more than a physical level. If you have nothing in common, or you think she's boring or annoying, there's no sense in moving forward. But if there seems to be commonality and interest, keep the conversation going! If one of you is leaving, tell her you're glad you ran into her that night and ask if you can give her your number (or email address or social media, whatever young people do, I'm middle-aged so I don't know). But the important thing is that you're offering her something rather than asking her for something. This means she can say no, or if she says yes, she still has the choice on whether or not to follow up with you. It puts the control in her hands which can make her feel more safe.

Good luck, I hear it's rough out there for folks your age.

I'll make idle conversation with anyone. Some people are down some aren't. I'm rarely trying for a date or romance. I just see where the conversation goes, sometimes to a date or romance.

Think the best advice is that when you talk to a woman in public you should have a reason besides her being a woman in public. Like if a man approached me because he thought my shirt looked cool or he saw me reading a book he liked that's a fine bit of casual conversation. If he just point blank asked if I had a boyfriend as if that's the only reason a woman wouldn't want to date a random man she knows nothing about I'd tell him that was none of his business.

I approached someone before the pan and asked for her number. She provided it and while it didn’t go anywhere, she complimented me for doing a real-life approach. But I’m twice your age, so I’d go with what peers your age tell you. The rules could be completely different.

Not being able to freely communicate with about half of humanity is definitely a handicap, lol. Nothing that can't be learned though!

I have lots of advice but I haven't so much as held someone's hand since 2005. So about twenty years now.

The only advice I have is find women your age and ask your questions to them. See what they say. Then go from there.

I like to talk to a room. i.e. i watch social cues to find an "in" then i try to start a public conversation?

You are both right and you’re both wrong.

I’m right in the middle of yours and your parents age. The dating scene is complete shit today compared to when your parents were in it. I don’t believe they’re likely recognizing how different shit is today vs 30-40 years ago.

I feel like the viewpoint you’re coming from is calculated, safe and fairly accurate for the experiences you’ve likely had in your teen years and early 20’s. More often than not, sticking with what you’ve been doing is going to be considered the more socially graceful, generally appropriate baseline behavior in today’s dating world.

If you were to take the opposite approach, and approach women in places that you’ve previously considered socially unacceptable, there’s a good chance you’d have some success and a good chance you’d deal with some awkward rejections too.

If I were you, I’d try putting myself outside of my comfort zone a couple of times, maybe a city two hours away from where you live. If you’re into anime or comics, go to a con and approach women you’d be uncomfortable approaching otherwise. If you’re into reading at all, go to a bookstore and do this. Everyone needs to eat, supposedly the grocery store is fair game.

Do some social experimenting. Safer to figure out things a bit away from home though if you’re nervous.

I'm going to echo the suggestion to approach men (and later women) for whatever reason to practice approaching people you don't "have business" with.

Ask a question, comment on something benign (cool shirt?), etc.

And also expand your list of contexts where it's ok to talk to people.

Anywhere that groups of people gather is a good option. Concerts, cafés potentially, parks...as long as you aren't cornering anybody, you should be fine.