Going through Syria first would still require going through Turkey. Basically to reach the closest significant Natural Gas Tie-point, they go to Ankara in Turkey. I don't see Syria as a real obstacle as it makes little difference in pipeline length. But I don't now the terrain, avoiding mountains could be a reason to go through Syria.
Iraq borders Syria. A pipeline can go to Syria without going through Turkey. But there are definitely geo-political gyrations going on beneath the surface here.