A reader builds an expectation with every sentence. When the next one reverses direction without warning, they have to go back and rebuild — and that rereading is exactly what a cohesion mark measures. The contrast connector costs one word and removes the need for it. That is all it does, and it is why the family matters more in a discussion essay than anywhere else: the entire structure of that essay type is a controlled series of reversals.
The family splits along a line that decides your punctuation, and the split is not about meaning. “However” is an adverb: it opens a new sentence, or follows a semicolon, and it cannot join two clauses with a comma. “But” and “whereas” are conjunctions: they join clauses inside one sentence. Writing “The scheme was cheap, however it failed” is the comma splice, and it is the most common punctuation error in Task 2 — produced by a word choice, not by carelessness with commas.
The third thing is strength. “However” is neutral. “Nevertheless” concedes that the first point had force and reverses anyway. “In contrast” sets two things side by side without preferring either. Choosing among them is a decision about how much ground you are giving, and it is visible to the reader whether you meant it or not.
“However” opens a sentence. “But” and “whereas” join clauses. This decides the punctuation, not the meaning.
“X, however Y” is two sentences joined by a comma. It needs a full stop or a semicolon.
“Despite” and “in spite of” take a noun. “Although” takes a clause. “Despite it was late” is the classic error.
“Nevertheless” admits the first point had force. “In contrast” prefers neither side.
