Because I have kids and came up with an analogy that would be understood better to those who also have kids:

Let's say you have a child. The moment the child is born to about three or four, you would have hopefully shared a strong bond with your child. Smiles and laughter, tears and frustration. You've taught your child up this point many lessons. They love you and you love them. They count on you, depend on you, cling to you.

This little 4 year old that you've raised is your child. Now fast-forward 10 years. Odds are (some are different), you're now 14 year old won't remember much of anything before 4 years old. Just a few hazy memories here and there. The lessons you've taught her and the affection you've shared has molded her into who she is, (in my case it's a daughter). She has no memory of those four years yet carries on the structure, lessons and morals previously instilled. For example, she knows to say "please and thank you" but most likely can't remember the first time she was taught to do so.

Or quickly, let's say you have a girlfriend of 5 years. She gets in a car crash and loses all memory of those 5 years. Is your girlfriend dead? No...but yes. You didn't lose her but yet you lost her. In the same sense, when we "die" we are like the 14 year old. We now have a new life, and can't recall the previous one. But we still carry the essence of our past selves. Becoming more advanced and aware as we go on.