That is a good question. The reason why "while Juanita went shopping" is not an independent clause is because of the word "while." "While" makes it dependent on some other action. In other words it is a temporal clause. If you changed the sentence and wrote, "Juan played football and Juanita went shopping," then the sentence would be two simple sentences connected by the conjunction "and". In short, the "while" makes all the difference. Get rid of that and then you will have a nice compound sentence. With the "while" you have a subordinate clause and therefore a complex sentence.
The sentence "Juan played football while Juanita went shopping," is a complex sentence.
The main clause or the independent clause is "Juan played football." It makes completes sense by itself and hence it is called the main clause or the independent clause.
The subordinate clause "while Juanita went shopping" does not make complete sense by itself. It makes complete sense only in relation to its main clause "Juan played football."
The subordinate clause "while Juanita went shopping" is an 'adverbial clause of time' because it tells us what Juanita did when Juan played football.
A compound sentence is a sentence with two or more than two main or independent clauses. Two main or independent clauses are linked by coordinating conjunctions like 'and.'
"Juan played football and Juanita went shopping" is a compound sentence with the two main clauses linked by the coordinating conjunction 'and.'