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Per comments, OP's instructors are probably just incompetent (or perhaps he somehow misunderstood what they meant). In standard English, and has two distinct meanings...

1: Dick liked Jane and she liked him
2: Dick insulted Jane and she slapped him

...where #1 simply uses and to join two "independent" statements - stripped of pronoun substitutions,...

1a: Dick liked Jane
and (another statement, with no specific relationship to the first)
1b: Jane liked Dick

But in #2 the conjunction implies a temporal/causal relationship between the two statements...

2a: Dick insulted Jane
and (subsequently - pragmatically, probably consequently)
2b: Jane slapped Dick

Grammatically/semantically, the and in #2 can be replaced by and then or simply then. Perhaps OP's instructors felt he was overusing the two-word form in contexts where it was pragmatically obvious that the second event was later in time and/or caused by the preceding event. But this is a matter of style, nothing to do with grammaticality.

TL;DR: Even if OP's instructors knew what they were talking about, they've obviously failed to convey the correct information to their student. The only reasons to avoid and then are (1) - if the context implies no [con]sequential relationship, and (2) - because using it excessively can result in a stilted prose style.