A sentence that is logical has a subject and a predicate. When a subject is introduced in a sentence, an expectation is set up about the grammatical direction the sentence is going in, and when that expectation is not met, the sentence does not sound right. Take this mixed construction example:

Teachers, a noble profession, involves a lot of patience.

Teachers are not a profession; teaching is. When teachers were introduced as the subject of the sentence, it created the expectation that the rest of the sentence would describe something teachers do or are. The predicate involves a lot of patience and takes the sentence in a different grammatical direction, making it a faulty predicate. We could rewrite the mixed sentence this way and it would be grammatically correct:

Teachers have a lot of patience.

However, the original sentence clearly intended teaching, as a profession, to be the subject, and the predicate was intended to show that teaching does indeed require a lot of patience.

Teaching, a noble profession, involves a lot of patience.

Of course, it would also be correct, if a little less elegant, to simply divide the sentence in two.

Teaching is a noble profession. Teachers have a lot of patience!

Sentences with mixed constructions can often be found in the first drafts of writing; the writer sets out with a stream of ideas that sound misconnected in the second reading. This is just one of the reasons reading over and editing your writing is always a great idea.