Why did they support that?
I can't come up with any explanation that makes rational sense.
As SaberTooth says it might be the case that an reelection - and if they didn't come up with a viable candidate for State Minister today the speaker had promised to call for reelection - would mean an increase of percentages for the Sweden Democrats (SD). However, if election/party support surveys were to be trusted, it also meant a decrease of support for every other party
except the Left Party (V), which stood unchanged, and the Social Democrats (S), which also had gained support.
There was the chance that the reelection might mean a Moderates-Christ Democrats-government-with-the-support-of-SD instead (or in a worse case scenario, if SD would have surpassed the Moderates as the biggest rightwing party, an M-KD-SD government). Which they of course would not want. But then they actually could have worked with the other parties, particularly the other left wing ones, to oppose right wing policies. Now we have a supposedly left wing government that has bound itself to
extreme right wing policy. I don't see how this is better. Especially in the long run, as I believe it will completely undermine people's belief in the left wing parties. It certainly undermines mine, but it is already pretty dug through to begin with.
And as I linked above, SD is already profiting from support flow from disenfranchised underclass and workers' movement demographics. They're going to profit from this too. So basically they traded a chance of SD gaining seats in the Riksdag for a chance of SD stealing their own voter base, all while supporting a government that has signed an agreement to
literally prevent the Left Party from having any kind of influence of politics. It's utter spineless madness.