Many people or a lot of people
Steve says, "There is this sort of shadowing technique. I just found that I can't continue doing it. But many people like doing it."
There are four basic ways of saying this:
Many people like doing it.
Many people like to do it.
A lot of people like doing it.
A lot of people like to do it.
Of course there are other variations. "But there are a lot of people who like doing it," for example.
In this case, "but many people like doing it" doesn't sound odd or different to me at all.
But if, for example, someone were talking about a concert and said, "There were many people at the concert last night" instead of "There were a lot of people at the concert last night," you're right, it would at least sound a bit stiff, if not foreign, to me. But if they said, "There were so many people at the concert last night," it wouldn't sound stiff at all. In any case, I wouldn't call it a mistake.
I'd argue that "many" is the more "correct" version. "A lot" is an informal variant, acceptable and common but not very high style. I wonder why you would consider that "many" is incorrect.
Of course you can use " a lot of" with both countable and uncountable nouns, whereas "many" is only used with countable ones ("much" is used for uncountable) but "people" is countable plural, so "many people" is absolutely fine
To elaborate a bit on ftornay's explanation, "many" is used routinely in newspaper and magazine articles as well as by newscasters. "Many people show up early at the polls." Many stores are closed because of the holiday." It is also used in conversations. It is a factual description of the existence of numerous countable objects.
By contrast, "a lot of" is more informal and is used conversationally. Importantly, it can be used to add an emotional twist. For example, John calls a friend to invite him to a barbecue. on the weekend. The friend replies, "Gosh, thanks for the invitation but I have a LOT of things to do to prepare for my business trip on Monday. Sorry." Using the term "LOT" and emphasizing it verbally, magnifies it and adds a slightly negative connotation. (Oh my goodness, , I have so MUCH to do!) If the friend merely said, "I have many things to do" it is more an objective description of the fact that he has numerous things to do.)
Another example: Mike placed an ad online to sell his bicycle. He tells a friend, "I got a LOT of calls!" How he says this expresses whether he is either very happy that he received so many calls or that there were so many, it was too much. Either way, the emphasis on "LOT" make the expression emotionally stronger (either positively or negatively) which the term "many" doesn't do.
One can drag out/prolong the pronunciation of the middle vowel of "lot" (L o o o o o o t") in addition to saying the word slightly louder for even more impact. (Doing this does not change the
pronunciation of the vowel. It is NOT like the double "o" in "moon" or "boom." )
Although "a lot of " can be said where all the words are given equal stress (a l o t o f ) as if it were one word, it frequently is used in speech when a speaker wants to strengthen the emotional connotation. This doesn't work with "many" because dragging out the "a" is awkward.
In conversations, native speakers instead would more likely repeat the word for emphasis: "I received many many calls." Still, while this would emphasize that Mike received numerous calls, it doesn't convey any nuance about how Mike felt about receiving so many calls. That's one of the reasons why the expression "a LOT of" is so useful in conversations because it does so often
add an emotional spin, depending on how the speaker pronounces it.
In texts, pronunciation cannot provide these nuanced meanings and so writers have to resort to other strategies (additional words such as "numerous, " an overwhelming number of") or punctuation (underlining, italics, boldface, etc.) to add emotional impact to "many" if desired.
Of course, all this is for more advanced learners of English.
"many people" and "a lot of people" are both grammatically correct. In the case Steve used above many is a synonym for lots of or a lot of. In fact, I'd argue that many sounds more intelligent in this context.