Does it mean you only accept today, giving no weight or importance to what was yesterday? Aren’t we all, today, what we were before today? Does looking at what we were give us insight into what we are now?
Why ignore our memories?
People ignore painful memories, they repress them. That’s a psychological problem and is quite severe.
Ignoring memories because you don’t like them, a bad relationship or a poor upbringing just suggests that confidence of thus person is questionable.
I think your questions kind of beg a distinction between examining past experiences [as with introspection or reflection], and compulsively dwelling in the past [as with traumatic experiences, for example]. The latter seems to be more a source of anxiety, where the former seems a better source of insight into one’s character.
I think people ignore memories for many different reasons, but the results usually seem, to me anyway, more detrimental than beneficial. The result, in very general terms, would seem to be ignorance. By ignoring a past experience we hinder our ability to understand and/or accept it, thus remaining ignorant of how that experience, and recollection thereof, affects our current behaviors.
I think it varies person to person. Some people seem to do fine never thinking about their pasts and cutting off memories when they come up or focusing on other things. This doesn’t work for me, but I don’t know what they need or what their goals are or even what their sense of self is. I have found that there is value in contemplating the past, along with pleasure and other feelings, but further that it is as if their are reactions I did not get to fully have in the past, for whatever reason, that if I allow them now, I feel better more alive, etc. I do find it gives me insight also, though it is more than that, it is making what is many parts into a single organism that I find most valuable about experiencing the past now.
BUDDHAHOOD IS ATTAINED IN AN INSTANT
I know a lot of people who ignore their pasts even to the point of never even wanting to see old friends again. I was born and raised in the Army and I’d often end a chapter of my life every time we moved. But I always remember the important people and the incidents that had an effect on me. I think that’s different than repressing memories. I’d end the chapters of my life because I knew, most probably, I’d never the people again. I also had the idea that, if I gave too much of myself to the people in my life, I’d end up with bits and pieces of me spread all around the world. My family–parents and sibs–were the constants in my life rather than any friends. Of course, now I have difficulty making friends, but I understand why. 
I think it’s of definite importance in introspection; and introspection, if done correctly, becomes sort of like self-analysis. Isn’t that what analysts are trying for? I’m fortunate in that I have basically happy memories; and, yet, I agree with you, statiktech. My questions do need to acknowledge the differences between examining past experiences and compulsively dwelling in the past.
Army brats have different ways of dealing with the rules and regs and the constant upheaval of moving. My years of rebellion were very short–like maybe, one–I’ve lived in the same location throughout my married life–and I’m a pack rat. It all has to do with the Military.
It’s interesting, to me, to realize that there are (it seems) so many people who ignore their pasts. Why I remember when … 
Santayana noted that those who do not learn from the past are doomed to repeat it. This is currently a favorite notion espoused by politicians. Beyond that sort of trivial usage of a profound insight is the recognition that the idea is valid for examining personal lives. The problem: to what extent one is able to see the past not as intolerable baggage but as what one was capable of doing or thinking back when. Those able to weed their gardens should be able to weed and prune their minds. And the past, if not kept sterile by obsessions, is both a reminder and an incentive.
Ier, the quote is actually “Those who cannot remember the past are condemned to fulfill it.” Whatever.
I admire Jorge Santayana because he approached philosophy in much the same way I do–or maybe I approach philosophy in much the same way Santayana did–from a literary stance–or view point.
We cannot know what we were capable of doing or thinking when we were children, we can only ‘know’ to what our reactions led us as we grew. Children are always faced with challenges along the way of their learning. Do we meet and greet those challenges, take them on and overcome them, or do we succumb to them in fear and uncertainty?
I seem to be crossing over among my thread about Fundamentals, this one, and yours about MI–but I see them as inter-related in lots of ways.
What I’ve found out about children–when bad things happen to them because of neglect or abuses of parents or persons in authority, they inevitably blame themselves for the harm they feel. They see adults as people who have arrived, who know what is best, who have gotten their act together, who represent what they , the children, desire to become. As adults the self-negations one learns in childhood become a source of incentive for escapes into destructive lifestyles, which are a toxic mix of drugs and harmful relationships.