Let me respond to each point that your dad offers:

Our not wanting to die is a bit of irrational behavior selected for by evolution. The universe doesn’t care if you’re there or not. The contrasting idea that you are the universe is mystical, not rational.

Others have questioned the use of the term rationality here, which is a good point to make. In my mind, there's a plausible distinction between rationality and wisdom, such that rationality is mastery of the means and wisdom is mastery of the ends (the definition of rationality offered on this site, of systemized winning, supports this--it isn't elaborated on what you should win, and on whether you shouldn't win one thing rather than another thing) . The above suggests to me, by analogy, that it would be irrational to eat when you're hungry, since hunger is an evolutionary bias. Given that hunger has produced in you the desire to eat, all else being equal, it is rational to eat. Similarly, all else being equal, if you fear death--live. But there are cases where other desires have greater priority.

Also, it is mystical to say that we are the universe, but not mystical to say that we are part of the universe. Nature itself seems indifferent and apathetic about our desires and needs, but given that we are natural beings, it must be true that our desires and needs are a part of nature. Even if immortality was an option for all of us, it might the case that another desire, for instance our love for another being, makes it more important that we die rather than live. But I think this calculus of ends belongs to wisdom and not rationality; rationality prescribes the best way to die, given that it is best to die. Sometimes dieing is winning.

The idea that you are alive “now” but will be dead “later” is irrational. Time is just a persistent illusion according to relativistic physics. You are alive and dead, period.

Does relativity really say that time is an illusion? I think the proposition that the duration of an interval time is relative to one's frame of reference isn't the same as claiming that "time is just a persistent illusion". When I fear my own death, I don't care about other frames of reference, only my own.

A cyber-replica is not you. If one were made and stood next to you, you would still not consent to be shot.

Ditto a meat replica

Truth.

If you believe the many worlds model of quantum physics is true (Eliezer does), then there already are a vitually infinite number of replicas of you already, so why bother making another one?

This is a different argument, that we are already effectively immortal. The desire for immortality should have already been satisfied. But obviously, our desire for immortality has not been satisfied, otherwise we wouldn't still desire it. Similarly, making another replica of myself wouldn't satisfy my desire for immortality, unless I thought it was me by some kind of a hive mind with my replicas. This is clearly not the case between quantum worlds. Therefore, we are not effectively immortal.