The Brazlian defender - who spent two successful spells at Stamford Bridge - was let go by incoming manager Frank Lampard in the summer, and he was offloaded to the Gunners in a cheap £8 million deal.
Speaking to ESPN Brazil, he said: "I was always very happy at Chelsea. And then the understanding of knowing that my cycle was over, even though I thought it wasn't going to end that way, in a quick decision.
"I decided to leave Chelsea before I even had my doors open at Arsenal.
"I know that Arsenal didn't come at a great moment, they had a weight on their defence, I go there and I'll have to pay the restaurant bill without having eaten."
However, Luiz was determined to "learn" and take his chance, even at the Blues' London rivals.
Reflecting on the move, he added: "But I'm going because I want something new for my life, I want to learn."
The 32-year-old defender admitted criticism over the Arsenal defence - and Chelsea fans' reaction to the transfer - made him doubt the switch.
He said: "My respect and love for Chelsea has always been true.
"It was difficult to deal with the emotional part, then playing, things were not happening on the pitch, the results weren't coming.
"[Former Arsenal boss] Unai [Emery] is a great coach and a great person, but things weren't happening for him either.
"So you get into a stir and try to stay upright and strong. And I often wondered why this decision was made. Why is this happening?"