I am trying to determine the right frame size for myself before purchasing a hybrid bike. My height is 174 cm and I have an inseam size of 85 cm. If I go by the height it should be a medium frame between 43-47 cm but if I go by the inseam height, recommended frame size is 58 cm! Apparently, the latter is wrong but I wonder why there is so much difference between two calculation methods.
Unless your body proportions are very unusual, I would expect two different calculation methods to produce similar results. But yours aren't. You're slightly taller than me, with slightly longer legs.
First, I'm curious where you found these two calculation methods.
Second, different manufacturers size their bikes differently. Bikes are sometimes sized by their "virtual" seat tubes, that is, the seat tube is extrapolated to a point where it meets a horizontal line extended from the top of the head tube (this is a holdover from when top tubes were horizontal, and seat tubes really were that long). Sometimes they're sized by the actual seat-tube length, and I've even seen one or two manufacturers size their bikes by top-tube length. So if you found one calculator at one manufacturer's site, and another at another's, you shouldn't expect they'd produce the same results.
My own guess based on your inseam is that you'd fit a 56-cm bike (using "virtual" seat-tube sizing), so 58 cm isn't far off. For a hybrid that has a significant slope to its top tube, I wouldn't be surprised if the actual seat-tube length were in the range of 43–47 cm.