We are too often not told why certain moves are ignored, as at the master level, such explanation is too condescending to the viewers, and they lose interest. So, to keep experienced players as active members, rudimentary explanations are usually abandoned.

In the present puzzle, there are a few moves that seem mysterious on the basic levels.

1...h3+
2. Kh1...
(why not 2. Kf1?...Qa1+, 3. Qe1 [forced]...R×e1#)
(why not 2. Kg1?...Re1+ ~
~~ [if 3. Rf1...Qg3+, 4. Kh1...Qg2#]
~ 3. Q×e1...Q×e1+, 4. Rf1...Qg3+, 5. Kh1...Qg2#)

(Back to) 2. Kh1...Re1+
3. Q×e1...
(why not 3. Rf1?...Re×Rf1#)
3...Q×e1+
4. Kh2...Q×f2+
5. Kh3...Kh5
6. b4...g4#

....Not sure if any typos here, but I don't have time to check it now....