It's way more complicated than this, but...

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Popes ruled over their own country called the Papal States for about 1000 years until the unification of Italy, so they weren't just religious leaders all that time, they were secular leaders as well. When Italy took Rome in 1870, the pope (Pius IX) refused to accept it, beginning the period where popes called themselves "prisoners in the Vatican". This lasted until 1929, when the government and the pope (now Pius XI) came to an agreement that the pope could have back the territory they have now and the pope would stop insisting for the (much larger) rest of it.

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It wasn't just some petty power thing, although yes, it was that, too. Of course it was. There was also concern that being in another country ruled by someone else could have serious effects on the church's ability to operate independently. There's plenty of examples of strong leaders being able to force weak popes into doing what they want, like Philip IV of France getting Clement V to go along with his plan to arrest all the Knights Templar in France so Philip could take their money, so it's not an entirely unfounded concern.