Thorgrim's point of view is that the Dwarfs are fucked. No ifs, ands, or buts. They're fucked, they're on the way out, they are stuck in an irrecoverable Tantrum Spiral that sees more dwarfs dead than alive every year at a rate that will see them extinct in a (dwarfen) blink of an eye. And he sees the countless Grudges that are not yet struck out, the lingering, festering wounds on the psyche of his people. His dying people, who are going to kill themselves killing everyone who has ever done them wrong whether or not he does anything. The deed that won him the contest to become High King, the act of restoring contact with the Northern Holds of Kraka Drak, an act of hope, was completely undone when they were wiped out by the Northmen. And by all accounts they died swinging, even though they could have fled southward, with the knowledge that their southern kin would have gladly taken them in.
That is the mindset we are working with here. A King who is so broken by the continued suicide of his people that the best he can hope for is for his people to die with a clear conscience and a good reputation with the umgi living in the flatlands beneath the mountains. The best he can do isn't to stop the deaths or bring hope to his people or even meaningfully reverse their decline; if there ever was a point of no return for the restoration of the Karaz Ankor, it was prooooooobably the Time of Woes. And they fucked it up good. As far as Thorgrim is concerned, he can't change anything except how they go. And he intends to do it slowly, while taking as much of the enemy with him as possible, so he can face the Ancestors and say that he did his best.
Belegar is just one more beardling in a long line of beardlings who thinks he's figured it out, who thinks he can overturn the decline of the Dawi and bring back the glories they had before the Time of Woes. I imagine that the majority of them died on their quests or died not long after with an orange crest and an axe in their hands. Belegar has a better claim than most to actually having the solution - cooperation with the mayfly races and throw cat ninja wizards at the many problems surrounding him - but Thorgrim is skeptical. Of course he would be. This man has been High King since not long after the ascension of the Great War Against Chaos, not long after Magnus the Pious became Emperor and reunified the Empire. This man saw the disastrous rule of Dieter IV. This man saw the way that the umgi insist on tearing themselves apart within as little as a single dwarfen generation. It will take a lot more than a reclaimed hold to restore the Karaz Ankor - and this is the same issue that Belegar has been grappling, mind.
Thorgrim shouldn't be hated or resented, though it is definitely fair and understandable to hate him and resent him. But he's a broken man working with broken tools, who hopes that he can at least do some good for his community before his workshop is finally closed down. Is it any wonder that when he hears that a recently reclaimed hold which doesn't even own half of its own territory, who didn't even have a Dwarf King manning the defense, was being attacked by four hundred thousand orcs and twice that in gnoblars to soak up quarrels and bullets and all the clever contraptions of the Rangers and the Engineers? Twenty to one odds, long odds for even the indomitable Dawi? After he already gave them a squadron of Gyrocopters? With all the other problems he has to deal with, because he's the bloody High King of the Karaz Ankor?
He doesn't mean anything by his letter. He's just given up.
Remember that - at least, if Thorgrim is anything like his canonical counterpart - the person who wants Belegar to prove Thorgrim wrong the most is Thorgrim.