Understanding Petrosian

Continuing An Obvious Positional Advantage, the diagram shows the position after the final move in the previous post. Petrosian considered that 'Black undoubtedly had the edge'. It doesn't matter how long I play chess or how much I study, I will never understand Petrosian's approach to the game. Black is an exchange down in the diagram, and Black is still better?

White continued 27.Be2. After 27...Bh6, Petrosian noted, 'Not the best. Black should have played 27...h5 first.' This is typical Petrosian; there is no explanation why ...h5 is better. Because the Bishop is sheltered against an attack on the h-file? Because the Black King gets a new escape square on h7? Because an eventual g2-g4 is prevented? All of the above or something else?

San Antonio 1972
Petrosian, Tigran

Portisch, Lajos
(After 26...Ne7-f8(xB))
[FEN "4rnk1/1bq3bp/1pNp2p1/pPnPpp2/2P5/5B2/P4PPP/1NRQ1RK1 w - - 0 27"]

The game continued 28.Rc2 Bc8 29.Nc3 Nfd7 30.Re1 Nf6 31.Bf1 f4. Of his last move, Petrosian wrote:

Here I was a bit hasty. Such moves require great caution. The e5-f5 Pawn pair has become less mobile, and the Pawn e5 can be blockaded. Naturally I had taken into consideration that my pieces (Nc5, Nf6, eventually Bf5) kept the square e4 under control, so I hoped to play e5-e4 safely. Of course, I should have taken some prophylaxis like 31...Kh8.

Considering the further course of the game, it is not clear why ...f4 is worse here or ...Kh8 is better here than in a move or two. What difference does it make? 'Of course, I should have taken some prophylaxis'; why 'of course'?

There followed 32.Rce2 Rf8 33.Na4 Nxa4 34.Qxa4 Nd7 35.Ne7+. Petrosian: 'I had overlooked this simple move.' Now the game was drawn after 35...Kh8 36.Nxc8 Qxc8 37.Qa3 Nc5 38.Qf3 Qf5 39.h3 1/2-1/2.

From this I understand that 34...Nd7, because it allowed White to exchange one of the dangerous Bishops, was an error. What move was better? 34...Bf5, or something else? Petrosian doesn't say. Three times the former World Champion criticizes his own play and three times I am left to wonder why. What a difference between his level and mine!