Coalition governments are a result of hung parliaments, when the country can’t decide which party most represents them. There is the question of whether coalition governments are a bad thing (most European governments seem to work OK with them), but we can debate that elsewhere.
In fact, AV tends to lead to similar numbers of hung parliaments to FPTP, partly because it is not a proportional system.
Patrick Dunleavy, of the London School of Economics, takes up the explanation:
At present a single party government is formed when one party has the most votes in over half the UK’s constituencies. Under AV a single party government will need over half the votes in over half the constituencies. This is a higher threshold, and so when UK voters have not clearly made up their mind to elect one party into power, AV may produce more coalitions – as in 2010, 2005 perhaps, maybe 1992, 1974 (both elections), 1964 and 1950. But minority governments, short-lived tiny majorities or coalition government happened anyway in six of these eight cases, except for 1992 and 2005.
When voters have clearly decided to elect one party into government, such as 1983, 1987, 1997 and 2001, then AV will not somehow produce coalitions. It will do exactly the opposite. In 1997, for instance, detailed research by LSE shows that the Labour’s majority under Tony Blair would have been greater under AV, and the unpopular Tories would have shrunk to only 165 seats (far fewer than they retained under first past the post). And the 1980s Conservative majorities at Labour’s expense would also have been larger under AV.
In Australia, over the past 90 years, the Alternative Vote has resulted in fewer hung parliaments than we’ve had in the UK.