Tangs or Sockets?
The funny thing about technological advancement is that it can sometimes go into reverse.
Take roads for example; the Romans really knew how to build them. They were famously straight as an arrow, but also layered to improve stability and drainage (coarser stone at the bottom, finer at the top). They were given stone drainage ditches and a gentle camber (like our own roads) and, finally, dressed with a hard-wearing flagged stone which would ensure they lasted for thousands of years.
Following the collapse of the (Western) Roman empire, it took us Europeans about 1400 years to remember how to build a proper road, and we all know how long they last before they're full of pot-holes and need fixing again...
Well, arrowheads are a bit like that.
The earliest arrowheads, often termed 'points', were made of hard stone (like flint or chert). Typically triangular or 'leaf-shaped', these flint points gradually evolved over time to become a bit more complicated, in that they were given a tang (an elongated bit to attach to the shaft of the arrow), and barbs (extended blades which did a lot more cutting on impact, and prevented the arrow from being removed).
And, so, the barbed and tanged flint arrowhead (as seen here) came to represent the highpoint of Neolithic ballistic technology.
Then mankind discovered how to work metal, and, ignoring the annoyingly inconvenient chalcolithic (or copper-stone age), the Bronze Age happened. It took a while for people to abandon flint arrowheads, mainly because archers in the Bronze Age were the poorest warriors on the battlefield - you had to be very rich to own a sword, and pretty well off to be a spearman, but archers were like the auxiliary slingers of the Roman period - expendable skirmishers who could barely afford their own armour.
Eventually, however, people did start to make bronze arrowheads, and they looked very much like the earlier flint arrowheads; being leaf-shaped or barbed, and attached to the shaft via a tang.
Then, at some point during the Bronze Age, the socketed arrowhead was introduced (spearheads of the time were already socketed, so producing a socketed arrowhead was inevitable) - and one of the advantages of a socketed arrowhead is that is can be very loosely attached to the shaft (the inertia of the arrowhead keeping the shaft in place during flight.)
Iron Age socketed arrowheads of Greek provenance, now available in the Timeless Galleries.
From the age of Sparta!
In fact, there are records of arrows being constructed on the field of battle just minutes before they were loosed at the enemy. The arrowheads would be affixed to the shafts with nothing more than wax. Then, once shot, if the arrow found its mark, the head would stay in the flesh. If it missed, the head would stay in the ground, or a tree, or whatever else it had hit.
In other words, they couldn't be shot back.
But what if the archer wasn't on the battlefield? What if they were in a forest, hunting deer or boar?
In that case, the archer might want the arrowhead to remain attached to the shaft. He, or she, would want the arrow to impede the target as much as possible and stay in the flesh; so, that person would be much more likely to use a tanged arrowhead, pushed into the end of the shaft and strongly affixed with resin or sinew.
A beautiful medieval tanged arrowhead available in the Timeless Galleries
Eventually, bronze gave way to iron, and arrowheads developed in all sorts of clever ways. Bodkin points were invented to pierce Roman chain mail; 'forkers'' (arrowheads with crescent-shaped blades - the points of the crescent foremost) were probably used to hunt wildfowl as the twin points of the arrow may have prevented it from skipping off thick plumage. Warheads, broadheads, transverse and tranchet blades; the types of arrowhead grew rapidly.
Then, the western Roman empire collapsed, and just like road building technology, people forgot how to make things - including the socketed arrowhead.
And so we find that the earliest medieval arrowheads were tanged. A little later, perhaps around (or a little before) the Norman invasion of England, socketed arrowheads made a reappearance. Then by the high medieval period we begin to see that diversity again: warheads, bodkins, Devizes swallowtails...
History, it seems, can be quite repetitive.