"I am not powerful enough to cast sixth-circle spells unaided, even if I understand them. I can't channel enough energy. I can cast them if I understand them and have an external power source. I had a scroll of Teleport on hand for emergencies even when I wasn't powerful enough to cast fifth-circle spells on my own.
When they're starting out, wizards become capable of channeling more energy on their own, over time, just through practice. But that method levels out around second circle and you can't get past third that way. But if you're using magic in combat regularly, then you continue improving on that front. Combat or - other emergencies, evacuating people from a disaster works as well as fighting in it, as long as you're using your magic, fast, under pressure.
The dominant theory is just that you have to be pushing yourself past your normal capabilities in a way that people are mostly not capable of doing deliberately in safety. And some people aren't capable of it even when in danger - most wizards are first or second circle. But it's frustrating because introspectively, I am mostly not pushing myself in combat, I actually try quite hard to do things calmly in the same fashion and from the same state as I do them in practice."