Why can't I progress the main quest?

Check which wall you have hit, because each one has a different fix. If the next quest asks for a character level you have not reached, you need experience. If your level has stopped climbing at all, you are sitting at a cap, and more experience does nothing until you earn a promotion.

Side quests are the third gate. When the main quest is stalled and your level looks fine, the missing piece is often a side quest that the story expects you to have finished.

Pushing ahead under-levelled is a poor workaround. Enemies well above your level gain damage multipliers and resistances, so you deal far less damage and take far more.

Getting the levels the next quest wants

Capturing Aniimo grants player experience, and the first capture of a new species in each area pays bonus XP. Catching species you have not caught in your current area is the quickest way to close a small gap. Treasure chests across the open world hold experience gems, so explore off the main path too.

Rank gates other content as well. Irisalis needs player level 20 and rank Student 1, and Journey Chronicles unlocks at Student I.

When your level will not move

A capped level means promotion. Finish four core courses within an Elite Training stage and you can attempt Title Promotion, which raises the cap. The linked article on Title Promotion covers the full system.

Not settled: Main story progress and promotion are tied together, and it is not settled which of them raises the Aniimo level cap. Some thresholds, such as the level 25 cap lifted by the assessment exam in the Sea of Flowers, are linked to promotion. So if your Aniimo stop levelling as well, do the promotion work before you go looking for a story fix.