When I was in high school, I was rather good in math, so my (not very well informed) advisors told me, "Oh, you should study engineering." Well, it sounded good, but I had no clue what it really meant. I grew up in a town with no industry to speak of outside of the petrochemical industry, and I had never known any engineer personally.
I started college and took freshman physics where I fell in love with classical mechanics. I said, "this is what I want to do." My teacher said that I should major in physics, but I was somewhat torn. I had been advised to study engineering, even though the college where I started did not offer engineering. This was back in the day when blackboards were actually black and we used chalk to write on them. After class one day, in conversation with my physics teacher, we were talking about what I should study. The blackboard was clear, and he turned to the board and began to write. At the very top of the board, he wrote "mathematician" and immediately under that he wrote "physicist." He then dropped a few dots down the board, and almost in the chalk tray he wrote "dime store clerk" and below that he wrote "engineer." He then explained to me that this was the ranking of the intellectual value of various careers. Dime store clerks were usually associated with being a high school drop-out, but he saw them as more intellectually valuable to society than engineers.
The next year, I transferred to a much larger university that offered just about everything imaginable, including engineering. I started there as a math major, but when I went to see my assigned advisor to have my fall class schedule approved, I had another surprise. I had indicated that I wanted to take second year physics, but my advisor, a world renowned mathematician, said, "My students don't take physics." I told him that I still wanted to take physics II, and I did.
At the same time, several of my friends from high school were studying engineering of various sorts, and I ended up sharing an apartment with a couple of them. I found out what they were studying, and it really looked interesting (mechanics of materials, electric circuits, electro-mechanics, statics, dynamics, etc.). In my "pure math" major, I was studying differential equations. We spent an entire semester studying the properties of the solution to y''+K^2 y = 0. Mind you, we never solved that or any other ODE, we only proved properties of the solution. I decided then that I would be an engineer.
So, my top three reasons are named Prof. Bob Brown (physics), Prof. R.L. Moore (math), and Prof. Wall (math). I've never regretted the change for a minute.