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I don't see any reason for Chelsea letting Pochettino go, he might not have got them to the top 4 as expected due to some circumstances of which any real Chelsea fan knows why, but then finishing in an Euro league spot is not bad for the team. It took Pochettino till almost the end point of the league to figure out the problem and fix it and even took them to the position they finish which wasn't expected by lots of fans. If you noticed many of his players started to understand his game plan and began to perform at their best, such players with same gameplan and additional players to the squad could've helped Chelsea secure a Champions league spot but a new coach with new gameplan might take them back to their previous state which would be very bad for the players and club entirely. I think those are the things Todd Boehly should've considered instead of wanting to terminate his contract, Poch needs a 2nd chance.
Pochettino has officially parted ways with Chelsea, ending a tumultuous season, and that has been confirmed on the club website. Club officials saw Pochettino performance from a different direction, the man from Argentina had been equipped with an expensive squad, but failed to bring home the trophy. Besides that, Pochettino could not convince the club officials by bringing Chelsea to finish in 6th place in the standings, it was not enough for save his job, and once again the club officials saw that a ticket to the Europa League was not worth the budget they spent in the transfer market. Pochettino ultimately had to part ways, after being evaluated by club officials.
Chelsea started with a poor performance, almost inconsistent throughout the season, fortunately towards the end of the season Chelsea experienced improvement, which ultimately led them to finish in the Europa League zone. Meanwhile, Pochettino dismissal did seem unfair, because many assumed that Chelsea would retain Pochettino, at least for the next season. The policy has been taken, Chelsea management will enliven the transfer window to look for a new successor to replace Pochettino. There is no news yet about who will replace Pochettino next, but the club must ensure that the next manager is able to manage Chelsea to compete with Man City and Arsenal.
Source :
https://www.chelseafc.com/en/news/article/club-statement-mauricio-pochettino