"I have been walking through mazes my whole life with my eyes closed, and I make progress by feeling the walls with my hands. In order to get through each maze I need to remember lots of facts about how the walls in the different mazes feel when I touch them. If I opened my eyes now, it would take too much time, and be too painful to adjust to the light. I never tried to open my eyes, and even though a lot of people keep telling me it's a lot easier to get through mazes with your eyes open, I think they are wrong. Besides, the few and far between times I get stuck, I can always ask one of the people who can see where I should go next. And if you think I need to keep my eyes open, then the next thing you are going to tell me is I should use my sense of hearing and smell too."
If you must reword and put his entire argument into a bad analogy, try this one:
"I've been walking through mazes all my life. This one time, I had to recognize a particular brand of poison flower, but I didn't know my flowers very well because flowers are rare in the maze."
And the answer?
"I asked my friend who was also in the maze: 'Is this flower poisonous?' He said yes. I said okay. We skipped the flower and moved on."
How often would I use this level of math? I know I use the others on an almost daily basis. Coming up with something I need linear algebra for, though? Few and very far between. Maybe you use linear algebra often, but most of us don't have a need for it.
And if you disagree, then I think you should actually know abstract algebra, number theory, topology, etc., so that when the next problem comes along, you can 'quickly come up with an optimal solution'.