Your father is correct, heavy squats and deadlifts ( especially the squats) do compress the vertebral column which can lead to compression of the intervertebral disc........but.......this compression also occurs from a host of activities, such as prolonged sitting, standing on ones feet for extended periods of time, and being overweight........and.......the squats and deadlifts do strengthen the muscles to such a degree that they protect even a thin disc--i have seen many, many older lifelong lifter types who come into the clinic at age 55 with some mild chronic back pain,,we do diagnostics and discover that they have a herniated disc that has been there for years,,but there back was so strong that it barely noticeable--and trust me a true herniated disc ( which is a generic and overused diagnosis) for an average man, would result in the average man screaming and writhing on the floor in absolute agony--I have seen it--not a pretty site. So its a trade-off, you strengthen the muscles, but can potentially weaken the disc.........however.......you can do a TON of simple things to keep the discs from being compressed--any type of decompression moves such as hanging from a chinning bar for 30-40 seconds following a lifting session ( been doing that for 30 years) do some athletic moves--high rep deadlifts ( with moderate weight) and best of all -hyperextensions and reverse hyper-extensions to lubricate and "milk" the disc--just getting movement in those joints will keep the disc healthy and fluid.....and there are other things which can weak the disc such as smoking and not enough water--both "dry" out the IVD and can put it into a vulnerable state.
One last thought,,,if a person has some pre-existing spinal problems, ie mild scolosis, and they squat and dead,,,those things can exacerbate the curve and cause compression issues down the road, much in the same way that a nail, which has very slight bend, becomes more bent as it is struck repeatedly by a hammer.
I hope that answers your question
have a great day