The more Charisma you have, the better you’ll be at, well, everything. Because that is what spells do, they do everything.
There are a lot of misconceptions about what is optimal in Pathfinder. The game has a very poor match between what it describes as good and effective, and what actually is. Players that take the descriptions’ word for things get misled about what works best.
Case in point, as described, magic isn’t everything. Non-magical classes are on equal footing, and even the most dedicated mage is well-advised to not completely ignore mundane concerns.
In reality, that simply isn’t true. Magic is everything. Having more and better magic makes you more effective—the only caveat being highly-asymmetric trades (more on that in a bit). This is the reality Paizo inherited when they based Pathfinder on 3.5e, and the reality they exacerbated by pretending things weren’t so. And this only becomes more true—much, much more true—at higher levels.
But people believe the descriptions. They want the system to be balanced. They even, at times, ignore evidence to the contrary. Or by limiting themselves to how things are described—healer clerics and blaster sorcerers—avoid coming across that evidence altogether. This may be what is going on with your GM.
Alternatively, or in connection, there is a consideration you GM might have that would be valid, in theory. Going from 16 to 18 in your point buy costs 7 points. That many points could, hypothetically, raise Constitution from 8 to 14. If you had to choose between 8 Con, 20 Cha, and 14 Con, 18 Cha, you'd be crazy to choose the former. Point for point, Charisma is much more important, but not three times as important as Constitution. After all, by mid-to-high levels, a bonus 5th-level and bonus 1st-level spell slot isn’t going to make or break you. Spells per day are cheap by mid levels—you will probably have enough. The DC is more important—1 more is the equivalent of two levels’ worth with a good save—but +3 higher Con is worth more than the 14 hp two levels of sorcerer gets you as early as 3rd level.
The problem with this analysis is that it’s in a vacuum. It arbitrarily forces your Con to 8, below where it starts, to maximize the effect. If your point buy were low enough that your choices were 8/8/8/8/8/20 vs. 8/8/14/8/8/18, yeah, going for the 20 wouldn’t be worth it—but your point buy isn’t that low. No one’s point buy is that low, I suspect—it corresponds to a point total of 2, when the lowest option Paizo gives is 10. You can, and should, get your Constitution to 14, but those points can, and should, come from somewhere else.
Dexterity would be your third-most important ability; the above applies to that too, but much less so.
As for the common suggestion that you could split the difference with a 19—whether or not that makes sense depends a whole lot on what level(s) we’re talking about. From 4th-7th, yeah, absolutely. From 8th-11th, 19 is just as bad as 18 so you might as well get more points out by going to 18, if that’s the route you’re going. And so on. Note that by 20th, you would typically have a +5 inherent bonus from wish or tome of leadership and influence to go along with the 5 bumps you get from levels—an even number, so starting with an even number is very valuable in that case. Anyway, depending on the level(s) you expect to play at, going with an odd number may make sense, but it’s at least equally-likely that this is a terrible choice that makes no mathematical sense. It all depends on how many bumps from level you’ve gotten.
Finally, please note that being optimal isn’t always necessary. Particularly for a sorcerer. You have power to spare and then some. You can afford to short yourself some on Charisma if you want. Your game may well go better, if otherwise you would overshadow the party too much. This answer really addresses the GM’s claim about the 20 being suboptimal.