Ah yes...the I/O blues...lack of maintenance...
what probably happened is the lazy or cheap previous owner, never had the drive pulled because it takes time and costs money. The bellows leaked let in salt water and rusted the gimble bearing to the shaft. Personally I'd let them do what they have to do to get it off, there are ways to do it using plastic wedges, ratchet straps but in the end, it may require expensive surgery.
BTW, on a properly maintained I/O boat this will not happen. I have removed my Cobra drive every season, this is 100% salt water and the drive just slides right off. It gets stored in the garage and re-installed in the spring. The gimble bearing, u joints and driveshaft splines get greased, the shift cable bell crank is checked and greased, etc. You should check the alignment with a simple tool and check the bellows for small cracks in the folds, when they appear its time to replace it.
The OMC Cobra outdrive is 32 years old. Works as new. I liked it so much I bought a spare Cobra drive freshwater used on ebay along with a spare transom assembly. If you own an I/O boat either learn to do this stuff which is not hard if you get an outdrive jack, or pay to get it done. Troubles will be chronic and expensive if its not done.
https://www.dropbox.com/s/qn3zrg0ruzwz2kl/Cobra drive install.jpg?dl=0
https://www.dropbox.com/s/nbiqnmzm0zmltaw/Cobra%205.jpg?dl=0
you can see what salt water use does, but with proper maintenance, it will last and be fine.