We wanted him when he was at Udinese, but he chose Barca. We wanted him when he was at Barca, but FFP stopped us making a serious bid so he went to Arsenal as it was the best offer on the table. The only other serious consideration came from Juventus who were in a period of recovery at that time, so Arsenal made perfect sense.
There's a few ways to look at the Sanchez 'statement' yesterday which are;
1. He's told Arsenal how much he wants to stay.
2. He's told Arsenal he wants to leave, so it's now up to them to reach an acceptable agreement with City.
3. If Arsenal refuse to sell him, he'll see out the final year of his contract & leave on a free next year.
Arsenal may take the view that they stand a better chance of reaching the CL next season with him rather than without him, so the £50 they'll lose in revenue will be made up by regaining a CL spot. There's also a view that if Arsenal have a good season, Sanchez may take the view that the team has sufficiently improved enough that he may want to stay after all.
I've learned over the years not to get too twisted regarding transfers. RVP, Hazard, Isco & Alves were all 'nailed on' at the time of the speculation, but none of them are here. Sanchez will happen if & when it happens.