Strong kings did emerge in Ireland - Brian Boru for one comes to mind - but there are several factors that stopped Ireland from becoming a centralised state. By the time Ireland enters written history in the 4th century, with the rapid conversion to Christianity, several factors were already apparent.

Ireland was heavily forested, and sea or river travel by 'currach' was often the best way of getting around. This is in evidence since the Neolithic at least (similarity of tombs in Newgrange and Brittany), and certainly in the Bronze Age, characterised by Ireland's inclusion in an Atlantic trade network with culturally and linguistically similar coastal settlements. Roads were not heavily developed; peoples in the interior of the island would have been quite isolated and 'backward' in adoption of newer technologies such as metal ploughs, the horse, iron, the quern, etc. Munster (in the south of Ireland) in particular suffered from this. Many people would not have thought of themselves as 'Irish' per se.

Ireland did not take to arable agriculture to the same extent as other countries in Britain. The grass was lush, and perfect for pastoralism. As a result, towns didn't develop in Ireland in the same way they did on the British Isle. There was quite a bit of transhumanism, and small villages and isolated farmsteads are the optimal setup for this. Allegiance would have been to the family and to the little piece of grazing land in the immediate vicinity.

There appears to have been a collapse in Ireland towards the end of the Bronze Age, and archaeologists are unsure as to what happened. Arable agriculture becomes much fainter in the pollen record, and it is believed that there was famine, plague and emigration as the population shrank to fit the resources at hand. Survival was the order of the day, wider contact the sole preserve of merchants and warrior groups.

The Iron Age did not impact Ireland in the same way as it did the rest of Europe, and the rise of iron over bronze meant that Ireland lost markets on one of its key exports - copper. The corresponding reduction in cultural contacts meant that Ireland slid into a Dark Age, from which it only really recovered in about the 3rd century AD.

The social situation reflected this. There were many petty kingdoms - as many as 200 at the time of Christ. Fortunes would wax and wane, and sometimes one king would rise to consolidate an area. This was a long, drawn-out process, similar to Sengoku Jidai in feudal Japan but with less knowledge of, and thus less ambition to unite, the whole island. By the time St. Patrick arrived, five or six kingdoms were dominating, with a lot of give-and-take and a lot of infighting.

Foreign incursions to Ireland were always a thing, and a scattered population without knowledge (or need of) more advanced weaponry (horse, iron swords, heavy armour etc) was easy prey to foreign invaders, be they 'Celts', Picts, Gauls/Britons fleeing the Romans, or Vikings.

Even the arrival of the Vikings and their subsequent colonisation did little to unite the Irish. It would take over 100 years for Boru to rise up, consolidate the larger part of the country, and drive the Vikings from Ireland. That's the narrative anyway. In reality, Vikings fought alongside Boru, and Vikings continued to live and prosper in Ireland after the Battle of Clontarf. Boru's death at Clontarf caused the High Kingship to splinter once more, and Ireland was ripe for the picking again. 150 years later, as the Normans set sail for Ireland, the High Kingship was still being bitterly contested. Perhaps if the island had had another fifty years free of external aggression, we'd be looking at a very different situation, and a man like Robert Bruce could have shaped Ireland's destiny.

Sources: Origins of the Irish by Mallory, History of Ireland in 250 Episodes by Bardon, Pagan Celtic Ireland by Raftery

Another reason for the lack of a single centralised state in Ireland was system of succession used by the Irish royal houses, tanistry. Unlike the kingdoms of Scotland (which initially used a tanist system but later abandoned it) and England, every male in an Irish ruling house was a possible heir.

The tanaiste (the heir to the king) was chosen at the time of the king's inauguration. The tanaiste was normally someone whose support the new king needed, a member of rival branch of the family for instance. However, the longer the king ruled, the more likely the tanaiste was to have already died, or his house may have lost its power, making it easier for another family member to challenge their right once the king died. Under this system, the potential for civil war, and therefore the chance of intervention by outside powers, was higher than under primogeniture.

These problems were exacerbated by the failure of the Church to enforce strong distinctions between legitimate and illegitimate offspring, and to discourage divorce. Therefore Irish rulers often left behind very large families full of rival heirs. After Rory O'Connor withdrew from the kingship of Connacht in 1183, civil war followed for almost two decades with his sons, brothers, and grandsons vying for the kingship. The English and Scottish practice of passing the crown to the eldest son/closest male relative of the king removed a lot of this uncertainty over the succession and the potential for instability.

Once the Normans arrived in Ireland in the late twelfth century, this situation only worsened. The Irish lordships lost much of their prize lands in the east and the incoming settlers began to exploit conflicts between the Irish, as the Norman Lacy and Burgh families did with the civil wars in Connacht.

If you wanted to read more on this, Robin Frame's work on the medieval British Isles would be useful. It's Four Nations History, so he tries to look at England, Wales, Scotland, and Ireland together and highlight and explain the similarities and differences. His book The Political Development of the British Isles, 1100-1400 (Oxford, 1995), has a chapter on the differing styles of kingship in Britain and Ireland.