Why is data in computer science considered to be discrete?

Question

I understand that "structure" of data is totally dependent on Boolean Algebra, but:

Why is data considered to be a discrete mathematical entity rather than a continuous one?

Related to this:

What are the drawbacks, or invariants, that are violated in structuring data as a continuous entity in $r$ dimensions?

I am not an expert in the field as I am an undergrad math student, so I'd really appreciate it if someone would explain this to me like I'm five.