I am thinking you have "double shielded" RG-6, takes a F connector with a large center and you most likely have F connectors for RG-59 OR may have Quad Shielded RG-6 connectors which has a smaller center.
Does the center look like it will fit the wire or is it too small or too large?
Quad shielded cable because of the extra shielding layers the center is a bit smaller in diameter and the outside jacket of the coax is slightly larger.
When you removed the jacket, how many layers do you see?
I suspect the connector package may be mislabeled or perhaps the wire is mislabeled?
If you actually have quad shield cable, it can be a real pain to install the connectors as the center of the connector must push not just 2 layers of shield but 4 layers.
They do make installation tools that you screw the connector on to and looks like a screw driver, gives you some added leverage.. I typically use any old two way or three way passive splitter for the installation tool gives me a better gripping surface than just the connector..