Why is cross holy? It is a symbol of the crucifixion, but Jesus did not say the Cross is holy, or in any place in the Bible the cross is holy and the cross was not holy before Jesus. Who prescribed the Cross as something holy?
The term "Holy Cross" refers specifically to the cross on which Jesus died, the place where he sacrificed himself for us to redeem us from our sins, and to reconcile us to God the Father. It doesn't refer to crosses in general, and not to any representation of the cross.
It is absolutely true that crosses in general were place of torture, pain, suffering a degradation, and it would be inconceivable to consider crosses in general to be holy. However in the case of Jesus' cross, what he did on it, namely his death, was a holy event - one of the holiest events in all of history, affecting every single human being who ever lived or will live - an act of unbounded love and self-sacrifice. In essence, the holy act that took place on that cross turned it from a degrading and despicable place to one of the holiest places that ever existed. It's that sense that the term "Holy Cross" is used.
If you are asking about the use of crosses and crucifixes as a symbol. the purpose of these symbols is to remind us of the holy act that Jesus made by dying for us. In that sense the cross is a holy symbol, because it reminds us of a holy act.
If you are looking for a parallel, consider maybe the cell in which Nelson Mandela was imprisoned. I am not trying to imply thatis necessarily a holy place. However, once a site of oppression, it is now visited by many, inspired not by the acts of cruelty and oppression which the cell was designed for, but by the tenacity and perseverence that Mandela showed while locked inside.
Not all Christians would agree that the Cross is holy.