Does it mean I'm really ugly if no guys ever approach me, not even old men?

I am an older guy (you are way out of my range), but I will comment.

First of all, if you want men to approach you, going to bars and clubs would be a good idea. I am curious why you don't go. I don't know about younger men any more, but I don't generally approach strangers (men or women) in public unless there is a reason.

The key to meeting people is to go do interesting things with people. Do you have interests where there are single men? Do you go to meetups, or to church, or to a kickball league.

This is also the 21st century. You can initiate with men too. Find someone interesting and go an introduce yourself. Men are as insecure as women... and many cool men are nervous waling up to women. If you went and said 'hi' something great might happen.

It's likely in your bearing and demeanor. If you are receptive and smiling, you will not just be pretty, you will likely attract men's notice.

I agree. Some women just naturally look unapproachable.

Sure... but if a woman comes up and starts talking to you, how do you respond? Or if a woman is with you in a group that does hiking, or biking or kickball...

The idea that women should stand around smiling and looking pretty and wait for men to approach them seems outdated to me.

Fine, but if they fit my picture of unapproachable, they just won't be approached by me. By the way, if they come up to me and start talking, they are very likely not to fit my definition of unapproachable. Unless they come on as hostile. In my life, hostility is not a welcome quality.

I get what you are saying.

I mean some women do put their nose in the air and come across as unapproachable, then there are the "shy" women who put their head down and as such, aren't appealing enough I mean what is it that attracts a man to a woman?

Either a show of interest or a show.

OP I suggest perhaps that you are shy and just don't love yourself enough to believe that you are beautiful inside and out and can make your own decisions on whom to accept a date with.

Go look in the mirror put some make up on, smile