Why do ATC instructions to change level include the words "climb" or "descend"? ATC instructions to change level include the words "climb" or "descend" depending on the direction of the vertical maneuver. For example, "Descend to 2500 feet" or "Climb to FL70".

For comparison, instructions to turn to a specific heading often, but not always, include the words "right" or "left". We can say "Turn right heading 120" or "Turn left heading 360", but in some situations we may simply say "Fly heading 180". When using "Fly heading", it is implied that the turn should made in the direction that requires the smallest change of direction. A pilot heading east instructed to "Fly heading 360" will always perform a left turn, even if the word "left" was not included in the original instruction.

Similarly, for speed control, we have phrases such as "Reduce speed to 220 knots" and "Increase speed to 280 knots", while we can also simply use "Maintain 240 knots", in which case the pilot will then speed up or slow down as appropriate.

Radio phraseology is designed to be as short as possible, and radio calls should include no excessive words. This makes me wonder, why do we always include "Climb" or "Descend" in level instructions? If a flight is at FL320 and we need to instruct it to get up to FL340, it is self-evident that the pilot must climb, not descend. Using this logic, a phrase such as "Maintain FL340" or even just "FL340" (Example: "[callsign], FL340") should suffice.

I can think of reasons who we do use climb and descend. It most likely improves situational awareness for both controllers and pilots (including other flights on the frequency). It could also enable pilots to identify situations where they mishear a level instruction (Example: for a flight on FL320, instructed to "Maintain FL240", the crew might mishear this and think they are cleared to FL340. If the phrase "Descend to FL240" is used, this is less likely to happen). Finally, "Climb to" and "Descend to" is not much longer than "Maintain".

However, this leaves the question of why we have such "neutral" phrases for heading and speed restrictions. Wouldn't enforcing the use of "Right", "Left", "Increase" and "Reduce" introduce the same benefits we get from using "Climb" and "Descend"?

Is there a historical reason the phraseology concerning level changes is designed the way it is - perhaps an incident or accident where another phraseology was used? Or is it a coincidence that level instructions are different compared to heading or speed restrictions?

I can come up with "qualified guesses" myself, so I am hoping someone with actual knowledge on the topic can provide a factual answer.
Adding the instruction "climb/descend" to the flight level is an example of linguistic redundancy offering a very rudimentary form of error detection for voice communication (which is inherently "unreliable", as it can be misheard by the receiver – on top of the sometimes poor ATC radio channel quality): 


  In […] telecommunication, error detection [is a] technique that
  enables reliable delivery of […] data over unreliable communication
  channels. Many communication channels are subject to channel noise,
  and thus errors may be introduced during transmission from the source
  to a receiver. Error detection techniques allow detecting such errors.
  (source)


Therefore adding the instruction "climb/descend" offers an additional layer of security, because


the pilot would never descend when instructed to climb (and vice versa)
and the pilot is able to detect an instruction mismatching the flight level, i.e. "climb to FL240" when already at FL320 (taking the example in your question)


... but not perfect security (because the pilot at FL320 would not detect an error if ATC mistakenly instructs him to "climb to FL420" instead of "climb do FL400"). Therefore ATC instructions are repeated on the receiving end by the pilot.

(For a non-aviation analogy, the same technique is applied when dates are agreed upon on the phone as "Friday, 4 January 2019", although the day of the week is already implied by the date itself.)

In essence, your question "Why do ATC instructions to change level include the words 'climb' or 'descend'?" can be best answered by the (limited) added information transmission security these instructions provide. Therefore for me the real question is why instructions concerning speed and heading don't obligatorily require this sort of disambiguating instruction – especially so as this unspecificity can demonstrably lead to confusion. I hope someone else will be able to answer this part of your question, as I don't have specific knowledge about this aspect of it.