Science is something that can be empirically proven. Two luxomancers can perform the same mental equation and get the same energy bolt, in this respect luxomancy and magus in general [i]is[/i] a science. Perhaps a better analogy would've been a biologist trying to give a lecture on metaphysics, except they're not any sort of physicist. If your character was a luxomancer they would be able to learn how to perform the spells of other luxomancers, not through observation or intuition but by being taught the processes by the luxomancers themselves: If you are [i]not[/i] a luxomancer, then it would take ten years just to get to the point at which you understood the theory behind luxomancy, and even then you wouldn't be able to cast the spells, given that yours is a different sort of magus. 
 
The reason magus is so diverse then is because, just like any group of sciences, there are veritable thousands of subdivisions of study and- much like when one is working towards their degree- it is a necessity that many Arcanists develop their own personal fields of study just as one would research their thesis. Two people may both be pyromancers, and both will be capable of conjuring generic fireballs and setting things alight. However if one devotes their study time to causing spontaneous explosions, and another studies towards spewing molten rock from their palms, the way they've achieved this is known only to them, and not the adjacent pyromancer. This isn't to say that what they're doing isn't an empirical science, it's just that they're studying two different areas of it: They could just as easily exchange notes, and- both of them having studied pyromancy- they would both understand. But someone who isn't a pyromancer and instead studied, let's say, Terramancy (earth manipulation) wouldn't understand a word of it, just as a biologist wouldn't understand a lecture on metaphysics.

Ibyxx has not studied pyromancy. He hasn't put the decade into learning its fundamentals, just as he hasn't put the decade into learning about umbramancy, luxomancy, opacamancy, auroramancy, necromancy or any other form of magus. Just because it cannot be emulated by people who don't study the same subject doesn't make it any less a science, if that were the case biologists and physicists would be mighty skeptical of one another.

Define illusionist.