To understand why Irish people in the preceding centuries might not have a pressing need for a written language we need to look at the sort of society that existed in Ireland, which, given lack of written evidence, means we need to rely on archaeology.

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While it's a little early for the time period of your question I feel it is relevant to point out that between the end of the Bronze Age in Ireland (c.800-700 BC) and the beginning of the "developed" Iron Age period in c.300 BC Ireland appears to have undergone quite the societal upheaval; Pollen records show that plant species from cleared areas shrink in relation to scrub and woodland species, possibly indicating a shrinkage in population. Settlements dating to this period are rather small, spread-out affairs with very few that show evidence of industrial activity. "Burnt mound" or Fulachta fiadh sites decrease in proportion to the earlier Bronze Age as well.

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Into the developed Iron Age around 300 BC we start seeing a greater range of settlement types and more complexity in their construction as well. We start getting radiocarbon dates from Crannóg sites as well as radiocarbon dates at what are known as the "royal" sites such as Emain Macha/Navan fort in County Armagh, Dún Ailinne in Kildare, and Rath na Ríogh at the Hill of Tara in Meath. These sites have multiple phases of occupation and are enclosed in some cases by multiple ditches. We also get more artefactual evidence from this period and a lot of it shows connection to the world outside Ireland; this is the period where we start to see La Tene style art in Ireland and we start to find high status objects such as swords, personal ornamentation like glass beads and bronze brooches, as well as greater amounts of more mundane metal objects like axes and knives. As well as this we get evidence of the results of what was almost certainly relatively large scale collective labour such as Black pig's dyke; a ditch-and-bank that runs discontinuously across a large part of the north of Ireland, possibly built to block the routes of raiders.

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So despite there being more evidence of complexity in society as we approach 0 AD we have none of the large urban or proto urban sites such as those seen in Continental Europe at the same time. For example in central France the Oppidum of Bibracte developed to hold a population estimated to be in the thousands, with dedicated 'industrial' districts.

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Things develop along more or less the same lines in the early centuries AD, we get further "Royal site" construction at Tara and at Rathcroghan in Roscommon but settlements stay relatively small and sparse with some being enclosed but with only handfuls of buildings in each settlement.

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To (finally) get around to your question, while it is really difficult to answer a question asking why some thing didn't happen in the past, it is possible that Ireland's low population, dispersed over a wide area, lacked the need for writing. Until chrisitanity, with a need for at least some people to be able to read the holy text, literacy and the recording of history wasn't something that was missed much in Iron Age Ireland. That isn't to say Irish people were ignorant of writing, Ireland was in contact with the Roman world throughout the first few centuries AD and Latin writing appears on items found in Ireland. Knowledge of Latin script influenced Ogham, the earliest script the Irish language was written in, and it came to be used in the 4th/5th centuries AD to record memorials or to indicate control of an area.

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Sources:

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Becker, K., O'Neill, J., O'Flynn, L. 2008. Iron Age Ireland: Finding an invisible people. Final report to the Heritage Council project 16365.

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Fulford, M., Handley, M. and Clarke, A., 2000. An early date for ogham: the Silchester ogham stone rehabilitated. Medieval Archaeology, 44(1), pp.1-23.