Were they unable to learn, or too set in their ways?
You've not been following the long posts on here have you?
The fact is that - under the circumstances* - there was no way for Haig to avoid fighting the Somme battle when and where he did, nor - under the circumstances** - could it have been fought more efficiently.
As for 'unable to learn' - the absolute reverse appears to have been the case. The Somme experience led to a substantial transformation of a whole range of aspects of British military capability, and laid the foundations on which Haig built (by 1918 ) an astonishingly large and proficient all-arms force to outmatch the Germans in all aspects of modern war, and which ultimately drove the Hun back to his own borders.
Seriously - read either (or both) of the two books that heve been recommended upthread (
Battle Tactics of the Western Front by Paddy Griffith and
Mud Blood and Poppycock by Gordon Corrigan) and you may find your way to a different understanding of the Great War,
* Germany having embarked on a meat-grinder offensive at Verdun to "bleed the French army white" Britain - in 1916 still the junior partner on the Western Front, remember - was obliged to try and divert some of Germany's military elsewhere. For the Brit and Commonwealth army that fought there, the Somme was a 'Come As You Are' party.
** The British national economy was still not fully mobilised: as a consequence Haig was stuck with what artillery already existed, and with the quantities and quality of munitions with which an immature weapons and munitions industry could supply his army, and could not in any case develop an advance from even the most successful attack, until it was possible to overcome the problem of bringing artillery fire support (with its vast logistic train) forward across the mess that trench warfare made of the battlefield. Wicked, wicked problems.