Learning two programming languages at the same time is definitely not comparable to learning Spanish and Mandarin at the same time...those two languages are so different that you won't gain anything from it. Learning, say, Spanish and Italian at the same time might be a better analogy, since you'll start to see word roots and constructions that are shared among romance languages.
I think learning more than one programming language at the same time is a great way to help you tease out basic programming concepts from the vagaries in the syntax of an individual language. How to types work? Scopes? Functions? Loops? Arrays? Hash tables? Those are all things that, once you really grok as separate from, say, whitespace problems in Python or curly brace issues in C, allow you to much more easily read and eventually pick up other languages.
Although I can't speak to learning two spoken languages simultaneously, learning a language similar to one I already knew (I knew Spanish, tried to learn Italian) was insanely difficult, because my brain couldn't distinguish them enough. It would get in a loop of searching for Italian words and running into Spanish words and then mixing them up.
On the other hand, learning German after already knowing Spanish was much easier -- and it was much easier to see the similarities and differences between the languages, because my brain would find the Spanish phrase while searching for the German one, and vice versa, but wouldn't get stuck in a loop about it.
I think learning more than one programming language at the same time is a great way to help you tease out basic programming concepts from the vagaries in the syntax of an individual language. How to types work? Scopes? Functions? Loops? Arrays? Hash tables? Those are all things that, once you really grok as separate from, say, whitespace problems in Python or curly brace issues in C, allow you to much more easily read and eventually pick up other languages.