Honestly, it's difficult to explain this. But in the same breath, it's extremely easy.
Christian use the cross symbol as a way to remember Jesus.
(Take 9/11 for example. Two big buildings stood there that was taken down in a terrorist attack. The government could have easily erected 2 buildings in the same spot to remember the dead. But instead, we have 9/11 memorial that's now visited by thousands of people every day as a way to remember that horrific day and keep in mind all those who lost their lives.
(Courtesy: Following Trusting)
Similarly, Christians use the cross as a way to remember the sacrifice of Jesus - why he died, how he saved the world.)
The death of Jesus is more than just about an unjustified trial and killing. It's about a sacrifice that Jesus made for the sins of humans. It's about how he saved humanity. It’s about the greatest compassion.
Everything about that day is revered as something of high relevance by the Christians and historians.
The cross now symbolizes Christ's sacrifice and all his good. It signifies the transformation between who we are and who we become when we follow him.
Of course, I am putting this in a very general way.
I am sure there exist many different reasons, including geopolitical reasons as to why and how cross became "the symbol" of Christianity.
But then if you think it intuitively, it’s not very difficult to assume why Christians revere cross instead of hating it since Jesus died on it…
That cross symbolizes much more than just death. And even when you’re talking about the death of Jesus, there are many dynamics you must understand, right FROM the "Seven Last Words From The Cross" TO the doctrines of salvation.
In simple words…
Cross symbolizes Jesus. Not just his death but his whole life. This is why Christian uses it to represent Christianity.