Out with the Old, in with the New. Good advice?

I'm not one to give advice, but I find that this is a flawed statement. "Out with the old, in with the new", is a little bit of a paradox in certain ways; if you go "Out with the old" to the extreme, that would literally mean getting rid of everything old, including memories. Technically, a statement, such as "Out with the old, in with the new", is a thought, and after that thought has occured, it becomes a memory.
Therefore, you forget the concept of "Out with the old, in with the new" because of itself. Then, in theory, you could fall into a vicious circle, a constant pattern of thought. You think of "out with the old, in with the new", so you discard the memory of that thought, either keeping you from doing so again, or, you think of it again, and again you force yourself to forget it.

That's only in extreme cases.

But, in certain cases, "out with the old, in with the new" can be helpful, to a degree. Objects, technology needs to be updated, serviced so that it keeps working. Sometimes, it needs to be replaced with the new.