He didn't pull out of the Arsenal job.
Arsenal blinked first, and punted for the more experienced option.
Arsenal interviewed him and respected journalists quoted him as saying he wanted control of the budget and when that didn’t happen he pulled out of the running.
Immaterial either way as any incoming manager would want to know the budget and the type of player the club were going to buy.
Would Mourinho take a job where he had 200m to spend but only on players under 23
I doubt it