The Irish became dependent on the potato because the Irish tenants had large families and largerly used second-rate land for their own crops. The potato can be grown in very marginal land that will not yield that much with other crops and offers a lot of calories (and other nutrients) for a rather low labour effort.

The absentee landlords (many of them British) grew a lot of other crops on their estates and raised cattle and had sheep graze for wool. Ireland produced all the food it needed and more, the problem was that the Irish peasants were poor.

During the 19th century, the common lands were divided among the lords and sometimes among the peasants by a series of enclosure acts in the British parliament. English free-holding farmers and tenants were often able to defend their right or add these lands to their farms or tenants, the Irish tenants had a harder time with this.

Much of the commons had been grazing land for cattle and sheep, and when the Irish tenants lost this they lost their ability to have a cash crop. A cash crop is something a farmer produces to sell for Money to buy equipment or things he does not produce himself. Cattle (to make cheese or butter), sheep (for wool), hemp (for ropes and cloth), pigs (for meat) and rapeseed (for oil) were common cash crops of the era.

When the Irish tenants lost their commons or had to pay higher tenancy fees to keep access to them (which they could not afford), their ability to produce cash crops decreased. The potato was the best option for them to feed their families and produce a surplus to sell.

Ireland as a whole was not dependent on potatoes anymore than England was - the landowners kept exporting grain and cash crops from Ireland even during the worst of the starvation - but poor Irish farm labourers and tenants were dependent on potatoes, and they suffered badly since they had no money to buy food since they had no cash crops.

Because the English owned all the good farmland in Ireland and used it to grow crops that they then shipped over to England to sell.

Do you mean the 19th Century, OP? The Irish didn't become heavily dependent on the potato as a part of their diet until the 1800s.