Under FPTP bad and unpopular MPs can often be impossible to remove. This can occur when the bad MP represents a party who have overwhelming support in their constituency.
Despite voters not liking or wanting the MP, under FPTP the voters feel obliged to vote for the MP otherwise an unwanted party may win the seat!
You may think well why not put up another candidate that supports the same party as the sitting MP? Effectively two candidates for the same party, the unpopular sitting MP and a new untainted candidate?
Well under FPTP this just wouldn't work -- it risks splitting the parties votes between the two candidates this could (again) mean that an unwanted party winning the seat.
However, under AV, this would work just fine... Voters could give preferences to both candidates -- knowing that if one is knocked their vote will transfer to the other - they can choose which candidate of the two they prefer with no risk of their vote 'letting in' a different party.
Some people have said that they think this an unlikely scenario (unofficial/independent party candidates running against official party candidates), but it has been observed that this is what happened when Ken Livingstone failed to be selected as Labour candidate for London Mayor in 2000, and Frank Dobson won their nomination. Ken (for better or worse!) ran against him was expelled from the Labour party but went on to beat Frank and won the office of Mayor. While 'independent' and as Mayor Ken applied to rejoin the labour party in 2002 finally being readmitted in 2004 and going on to be the official Labour candidate that year.