As I showed you in that example, candidate B is the majority winner because B beats A by a majority, and B also defeats C by a majority.
However, if we use alternative voting, instant runoff voting, then we'd look only at first-place votes, so 40% vote for A, 35% vote for C, and 25% vote for B, we notice that B, who is actually the true majority winner, is eliminated under alternative voting. That's because under alternative voting, if no candidate gets a majority of first-place votes, you eliminate the candidate who has the fewest first-place votes, and that's B in this case.
This example encapsulates the difference between majority rule and alternative voting.