Okay, is your friend arguing imagery or mechanics?
If he's saying a spear doesn't "fit" with full plate in an aesthetic sense, I disagree. The spear was a very common weapon historically, and it was used by knights as well as everyone else. The lance, in fact, is basically just a modified spear.
Now, if he's talking mechanics, that's a different story. A longsword does the same damage as a spear, plus you get the AC bonus for the shield. True, the spear grants you an extra 50% on Strength-based damage, because it's wielded two-handed. But then, if we're talking pure mechanics, a greataxe or greatsword is an even better option, because you get the extra Strength and those weapons do more damage.
In this case, even a longspear's reach isn't much of an advantage, because even moderately old dragons are usually large enough to have reach.
I happen to love spears, in terms of imagery, and I wish they were better weapons mechanically than they are. So, in your character's case... Image and feel, spear good. Game mechanics, spear probably not your best choice.