"Not having time" is a bit of an excuse, I feel. We all make time for the things we want to do or we feel, are needed to be done by priority. But it us who decide in the end, which ones we have to do. If you really want to do something, that becomes your priority and therefore you have time for that and you don't, for the ones which are not your priority.
So, effectively one could say "having time" is "making time". And actually we do have time for the things which are most important to us. "Not having time" is like an excuse like the term 'sorry'. Just by saying it, we often act as if that is supposed to compensate for our actions, but it is hardly so in actuality, more often than not.
There are times when we actually believe that it is not so. We are not doing something because we really don't have time. But somewhere at the back of the mind we know that what we are doing is important to a bigger picture which we might not admit openly. That's why we are doing it instead of something which we are apparently openly admitting to want but it isn't necessarily what is most important to us at that instant.