Another interesting topic on a genealogy site like Ancestry is the idea of public vs. private family trees. Ancestry lets you change this setting yourself.
A "public" tree isn't open to anyone in the world, but only to other Ancestry members, or individuals the tree owner has invited with a special email. People who the tree owner has marked as "living" have their info automatically hidden so you just get a block that says "private" instead of the usual names and dates (the tree owner can give specific individuals the ability to see living people).
A "private" tree is one that no one at all can see any part of, unless they have been specifically invited to by the tree owner. There are occasional workarounds for seeing part of a tree--I don't know if they are features or bugs of the site--but for the most part, if a tree is marked private, you are not getting any info from it. The idea is that you contact the owner and ask them to share the tree with you (invite you to see it), but of course they might not respond at all, or they might say no.
The idea of a public tree is that other Ancestry users can see the information and supporting records you've put together, and use that to help in their own research, copying individuals to their own tree. If you do it right you can get a person, their spouse, their kids, their parents, and their siblings saved to your tree in basically one step, with the names, dates, and places that the other person had on their tree (but not any of the records, like the census, or other notes--you have to put those on yourself individually). This is really the whole point of the site.
So someone who has a private tree, is basically able to take stuff from other trees, but without giving anything back, and some users feel pretty strongly that this is not good. I don't feel THAT strongly, but it is annoying when I hit a private tree. Usually I have so many lines of research I can pursue that I just bump up against that wall, bounce off, and move away in a different direction; or if it's something I'm really curious about, I'll send a message to the person asking for access, and hope they respond positively some day in the future.
As for why people have private trees, I know one person who puts a lot of tentative research on her tree (because this helps with the search functions of the site--it is much easier to look up records about a person in your tree, than to look up records based on info you've typed into their search engine freestyle) and doesn't want others to think it is solid info, and copy it, and have it be wrong later. It is very easy for misinformation to spread among the trees, because so many people just take other people's info without really thinking about it themselves or backing it up with records. So I know at least one person who is very wary about this and doesn't want to make her tree public until the main part of it is solid.
Other people's reasons, I don't know about. The default setting is public, so you have to proactively make it private if you want to.
I was thinking about this because I was updating my notes and recalled an instance where the Ancestry software said we had a common ancestor, Robert Smith 1752-1800, but because the other person's tree was private, I couldn't see their path from Robert Smith to them. I contacted them about sharing their tree with me, or telling me the path, and they were just like, No. I mean they had more to the message, and seemed interested and reasonably friendly, but all she would say was that she was descended from Robert Smith's son William (while I was descended from his daughter Elizabeth), and nothing else, even though most of the people involved are long dead. (I am fine if people keep private the names of still-living people, like a parent, and anonymize their own name.) And she'd "get back to me" if she learned anything else. Like, okay, fine, be that way. It's not something I obsess over--I had completely forgotten about it until I reread my notes--but I think it's a rather silly way to behave in the setting. So many people don't answer messages at all, I'd rather they just say nothing, if they aren't prepared to actually share anything useful. That just makes things a lot easier.