I think you mean "you can't install any software you want" and your parent means "you can install lots of pre-approved software" and you're both right.
At the same time I don't think installing arbitrary software is an essential feature of a laptop. These days most users rely on app stores or package managers.
Apple's iPad has been marketed as a laptop replacement and with its smart keyboard and the amount of apps it doesn't seem a long shot to me.
It's a laptop replacement for some people, some of the time. Which imo doesn't make it a laptop replacement. Because it would make phones from 10 years ago also a laptop replacement for some people, e.g. Teenagers who only use a web browser and some social media.
The key feature of a laptop is that you are guaranteed that it can do what you want. Even if you haven't thought of it beforehand. For example, a photographer buys an ipad pro. She reasons it should be fine since Adobe photoshop has been deemed worthy by Apple. For the first couple of weeks she is happy but then she wants to do some 3D work in bender. Oops blender isn't available on ipad and there is no way to make it work. Her laptop replacement isn't a laptop replacement at all since now she needs a laptop as well to run blender.
For almost every person such a scenario is certain to occur at some point. If Apple markets it as a laptop replacement it should be able to replace a laptop at all times.