I'm sorry but your professor was wrong. Mendel self-fertilized his pea plants and that is actually one of the experiments that formed the basis of what we now know as the heredity model.
The filial generations (F1,F2, etc.) are based on the premise that the parents are true-breeding for selected traits (originally).
In "classical" Mendelian Genetics the F1 will have dominant trait expressions (assuming no incomplete dominance), again, assuming the parental stock were true-breeding for said traits. The F2 gen consists of interbred individuals from the F1 gen and is the most diverse due to the expression of recessive alleles, allowing for 3 possible phenotypic expressions. After the F2 gen, depending on what traits were selected for/individuals selected, expression becomes more restrictive with each successive generation, generally. One can usually get a true-breeding individual by F4 or F6 if they properly identify their traits.
F2 and F3 gens by definition can NOT be back-crossed. F2 can only be obtained from the interbreeding of individuals within the F1 gen and F3 only from individuals within F2 gen.
If the parental stock were homozygous dominant for selected trait(s) then you would get "stable" or true-breeding Individuals in the F1 gen.
Now, this is all more of a guideline because in reality there are codominant traits, sex-linked traits, etc. and so many other facotors at play. People are usually not using true-breeding parental stock to begin with anyways. They'll cross F2's from one line to F3's from another and call their progeny F1's. Not hating or anything, that's just what they do. I'm not going to pretend like I don't chuck pollen too, it's fun, I just don't call the progeny F1's.