They wanted to make it in Innsbruck but they had a referendum where as everywhere the people were against the olympics. The Graz option was really only the last hope of the ÖOC knowing the chance to get these olympics was huge.
And also to be honest, I'm not surprised about the outcome of the Graz bid at all. It was doomed before it even went official. Innsbruck is in a winter sport crazy region perfectly located and able to organize olympics without big costs, while Graz would have had to build a lot more and is quite far away from the actual winter sport regions. From the first moment onwards it has always been clear that neither the country Styria nor the state Austria wanted these olympic games, that the city would have to organize the Olympics on it's own only with help from the towns where some of the events would have taken place. It was a complete mess that only could have worked without a referendum (as it was planned) but half the population of Graz would have protested if they had actually decided something that important without a referendum.
The problem is that because of huge olympic games like Sochi and the bad economic news surrounding those games nobody wants to host olympics anymore. And that's stupid. I mean of course I want olympics in Austria, I'm an Austrian winter sport fan after all, but putting that aside, the costs for Olympic games where no new venues would have to be constructed would be tiny compared to what happened in Sochi. IIrc there was even a study that showed Innsbruck would earn as much money with olympic games than they would have to invest without including the marketing value. I mean just think about that, basically hourlong advertisements shown in the whole world over two weeks and you don't have to pay for it. This development just makes me angry and I already fear the 3rd eastern Asian olympic games in a row where I'll have to stand up at 2 am in the morning.