Since around 30.000 years ago the human brain used to be bigger in size (with Homo neanderthalensis having the biggest brain size. Since then the average brain size has been a shrinking over the past 28,000 years), a friend of mine claims that the potential intellectual capacities of mankind have gone down (because there is a correlation between brain size and intelligence).
This seems very counterintuitive to me, but I couldn't find any facts or arguments to prove the opposite.
Does anyone have an explanation for this? Thanks in advance!

It is incorrectl to equate brain size with complexity and neuronal density and thus by extension (with no hard scientific evidence for that) intellectual capacity. As an example of this, by wight or volume the whale or elephant brain is much larger than a modern or neanderthal human.

Intelligence in man let alone other species if very complex and difficult to measure - trying to relate that to the number fo neurons and synapses is virtually impossible at present.

simple answer to your question and as you correctly imply, there is no evidence that the reduction in cranial volume is related to intelligence (however that is measured).