Apologies if you’ve answered this question before, but what exactly is tyrion trying to accomplish by encouraging aegon to go to westeros instead of on to meereen?

Tyrion has many reasons for doing so: it screws over Cersei (who he hates), it screws over Illyrio (who he hates), it screws over Jon Connington (who he’s not exactly fond of), and it ensures that Aegon won’t ally with Daenerys before Tyrion has an opportunity to gain her good graces by helping to save Meereen, allowing himself (who he hates) to become part of her inner circle.