The reason Mbappe left PSG was basically to win Champions League title. He did his best to win it at PSG but seems luck was never on the luck of PSG because I don't see anything that stopped them from winning it for several years that they assembled the best players in the world. There was a time they had Messi, Neymar, Mbappe and Di Maria in the same team yet they could not win it. Maybe Mbappe have realized that it may not be easy for PSG to win it, the reason he left for a team that have better records and chances of winning it. His decision to join Madrid have nothing to do with bad performance at PSG where he was almost worshipped.
Mbappé's move to Real Madrid has been rumored for a long time. It is still not clear to us why one of the best stars of the time, Kylian Mbappe, left his former club Paris Saint-Germain. We hear from many that he had the opportunity to win the Champions League while in Paris but failed to do so and joined Real Madrid to end that regret. Others have said that playing for Real Madrid was his dream for which he left Paris club PSG. Every transfer season we hear that Mbappe will leave PSG but after many such rumours, it never happened.
Finally, this season he joined Real Madrid as a free agent from the French club. Despite his young age, he has achieved the glory of touching many major trophies for the national team as well as winning the FIFA World Cup Golden Boot once, but his Champions League dream is still alive.
Mbappe's decision to leave PSG is based on his own personal interest but that not withstanding at least he has done very well for PSG and helped them win the Ligue 1 title on several occasions so he has already had the dream of playing for Real Madrid but PSG were the ones that upholded him for a long time if not he would have joined Real Madrid earlier than he did and we should not be questioning his decision to move to Real Madrid because he never moved out of PSG because of any pressure, it was after the expiry of his contract with the club which also shows that Mbappe has strong love for PSG. The only difference between his move to Real Madrid than when he was playing for PSG is that he can have the opportunity of winning the Champions League with Real Madrid sooner than if he had decided to stay back at PSG