This verse it typical of Jesus's use of double meanings and reversals. The main play on words here is the contrast between raising and lowering. Playing on the ideas of "higher" and "underling" in the previous verse.
The second phrase in this verse is identical to the first but reverses the verbs and their forms. This is captured better in the NIV version, which at least translates the word "humble" consistently. The first part echos an earlier such phrase, Matthew 18:4. Some of the sense of it being a parallel is lost because there KJV translators translated the same Greek word for "humble" differently in the first phrase and the second.