Copyright on content exists, regardless of how the uploader uses it.

And whether you upload part of a concert or performance- it is copyrighted to someone (and, in the case of live concerts, possibly even prohibited by the venue where the concert took place). Using their content without their express permission or licence- it can be claimed by them. They can claim it and YouTube collects ad revenue for them. Or they can claim it and ask YouTube to remove it (and you get a strike. Three of those and you're out).

Setting a video to private doesn't change copyright law or YouTube's policy. If it is uploaded without the copyright holder's permission/licence- it still violates their rights and they can act as above.

If you want to keep your memories- pop them on a memory stick or DVD. Then you can watch them whenever you like and no one will be any the wiser.