The idea behind risk asymmetry is that it occurs when two risks are present for a decision, but they are not equal in their magnitude. How it applies to sacrificing and saving now. While this is somewhat a simplification, there are two risks associated with the decision about whether or not to save as much as possible when you are young.
Risk 1 - You could save while you are young, sacrificing things you could have bought, then you die early, leaving that unspent money to your family, friends, or a charity.
Risk 2 - You could not save while you are young, buying things that probably are not that important anyway, and then face a financial crisis (major health problems, becoming too old or sick to work) when you are least able to address it.
Again, this is a simplification, but in this situation the risk associated with the two possible outcomes is not equal. The first risk is undesirable, but really is not that big of a deal. The second risk, on the other hand, is a big deal. While it is far away, being old and not having enough money to live on is not a pleasant situation for anyone.