Why did Hitler order counter-attacks as late as 21/04/1945?

Hitler was still trying to act strategically

Although popular history, influenced by memoirs of surviving German generals, tries to pin German defeat on Hitler irrationality and supposed madness, in reality it was not so. All controversial decisions made by Hitler (go to Kiev in 1941, drive on oil fields in 1942, various no retreat orders, remain on Crimea in 1944 etc ... ) had some grounding in reality, and were not made by whim. Instead, Hitler usually conferred with his underlings and various advisors, including the members of German High command (OKW).

Anyway, in April 1945 situation was dire, and Germans, including Hitler, were aware they could not win against both Western Allies and Soviets with emerging Communist Block (Poland, Yugoslavia, Romania, Bulgaria) . What they did hope was repeat of Miracle of the House of Brandenburg, which happened in 18th century and saved Prussia of Frederick the Great - Russian empress (czarina) Elizabeth suddenly died, and her successor Peter III led Russia out of war with Prussia. In an essence, Germans hoped for opportunity to somehow achieve separate peace with Western Allies, and maybe even latter somehow persuade them to join fight against World communism. Germans also hoped that Soviets would soon exhaust their human resources (actually not far for truth considering tremendous Soviet casualties ) and when that happens would be forced to stop their offensive. Considering what happened later , i.e. Cold War, eventual recreation of (West) German armed forces and many Wehrmacht and Luftwaffe personnel serving in it, even being high officials of NATO , again there is some grounding in reality for all of this.

German hopes were raised when Roosevelt died on April 12, 1945 (Czarina is dead !), his successor Truman seen as possibly more anti-communist and therefore susceptible for separate ceasefire agreement. Germans also most likely correctly assumed there would be a stop and demarcation line for Western advance into Germany (for example river Elbe). Therefore, if they somehow stop fighting British and American forces, and repulse Soviet forces with sufficient territory still in their hands, they could start negotiations from position of national government that still has some levers in their hands. But in order to do that, Berlin, as a capitol and important psychological symbol would have to remain in German possession. Without Berlin, German resistance would be split into pockets (north and south) without clear national center (larger cities in the West already being occupied, as well as Vienna) .

Therefore, although from operational standpoint unreasonable, from strategical point Hitler played only remaining move. Steiner's attack, if successful would potentially allow the Germans to retain control of Berlin, and prevent Germany of being split in two (as historically did happen ). Without Steiner's attack (which historically did not materialize) Berlin was certainly lost and war ended soon. Now, it is very unlikely Steiner would have changed anything if he did attack (except increasing casualties on both sides) , but theoretically there was a chance although minuscule. Ultimately and wisely, Steiner decided that war is already lost and choose to surrender himself and his units to Western Allies, thus dashing last hopes of some kind of victory.

Because the 9th Army of SS General Felix Steiner existed, but only on paper.

At full strength, this army could plausibly have taken on the First Byelorussian Front. But General Steiner balked because he was outnumbered 10 to 1 by this Russian unit (rather than say, 2 to 1, as might have been the case earlier in the war).

At this late date, much the same was true for other units Hitler ordered into action.

I'm looking for rational motives from a military standpoint

It might be a lot more "rational" if you apply a different kind of logic. We like to think of military strategy of something that is a task in optimizing all the resources you have to gain an acceptable outcome, where one of the acceptable outcomes might be honorable defeat and maybe capture. Normal rationale strategy dictates to preserve resources even in a loss because you might need them to fight another battle or even another war later.

Hitler's point of view on the outcome was more fatalistic and rightly so. Losing the war meant losing his life. The only thing he cared for. He did not care for other people's life or "pursuit of happiness". So if the military leader answers the question "is it worth a thousand lifes to delay the inevitable defeat another day?" with "Yes, it is" then all you see on military strategy, that looks foolish to an professional general that sees defeat as the least favorable, but survivable result suddenly makes a lot more sense. Volkssturm? Sure. Every bullet they catch saves the leaders life another minute. Pointless, 0.05% chance of success counterattacks? Sure, 0.05% is better then nothing and nobody gets anything from them surviving the war. Optimize for the chance of the military leader to live another year, month, week or hour and set the cost for everything else to zero and you reach a point that looks foolish to others.

It's not without rationale, it's just not our rationale.

Sources for the claim that Hitler valued the preservation of life in a case of losing at basically zero:

Just look at the Nerobefehl (German Version has more details). Albert Speer cites Hitler in the Nurnberg trials:

„Wenn der Krieg verloren geht, wird auch das Volk verloren sein. […] Es sei nicht notwendig, auf die Grundlagen, die das Volk zu seinem primitivsten Weiterleben braucht, Rücksicht zu nehmen. Im Gegenteil sei es besser, selbst diese Dinge zu zerstören. Denn das Volk hätte sich als das schwächere erwiesen und dem stärkeren Ostvolk gehöre dann ausschließlich die Zukunft. Was nach dem Kampf übrigbliebe, seien ohnehin nur die Minderwertigen; denn die Guten seien gefallen.“

Rough translation by me:

When the war gets lost, the people will be lost. [...] It's not neccessary to preserve even the basics the people need for their most primitive survival. To the contrary, it would be better to destroy even those things. Because the German people have proven to be weaker and the stronger eastern people will own the future exclusively. What is left after the fight are only the inferior anyway, the good all died.