How did “equivocal” come to mean what it means?
Solution 1:
Equivocal does not mean the opposite of unanimous, nor has it reversed its meaning.
For a person to equivocate is to use ambiguous language, and be non-committal: to "hedge" between two positions without committing to either, and (literally) to "call equally one thing or the other" — to talk equally of two different positions.
Equivocal is the adjective form: an equivocal statement is one which talks equally of two different things, and does not take a clear single position. Unequivocal is the opposite: something with no ambiguity, something that does not equally emphasise two contradicting points, a strong message which leaves no doubt.
Note that these words are generally used to statements coming from one person; they are not (necessarily) related to whether an opinion is unanimous or not. Unanimous just means, as you said, that everyone shares the same opinion. So, when used for a statement made by a committee, all possibilities exist: it may be
- unanimous and equivocal: everyone endorsed a vague statement (most statements by government committees are probably examples)
- unanimous and unequivocal: a strong position that everyone shared
- non-unanimous and equivocal: not everyone agreed with the statement, probably because some of them wanted to pass a clear message instead
- non-unanimous and unequivocal: a strong message that not everyone agreed with.
So you see they are orthogonal, not opposites.
Solution 2:
To support ShreevatsaR's point and to address the actual origin of the word, here's what Etymonline has to say:
equivocal c.1600, from L.L. aequivocus "of equal voice, of equal significance, ambiguous" (see equivocation) [...]
equivocation, late 14c., "the fallacy of using a word in different senses at different stages of the reasoning" (a loan-transl. of Gk. homonymia, lit. "having the same name"), from O.Fr. equivocation, from L.L. aequivocationem (nom. aequivocatio), from aequivocus "of identical sound," pp. of aequivocare, from aequus "equal" (see equal) + vocare "to call" (see voice).
Emphasis added. So equivocal never referred to "same voice", but rather to "identical sound". The difference might seem subtle, but it's crucial. Equivocal is not (and was never meant to be) about voicing the same opinion, but rather about voicing an opinion that could be taken to mean completely different things to different people.