/u/Malicous_Latvians and /u/gothwalk have given a good answer to this question here. Basically, Ireland's land is poorly suited for growing crops, and potatoes will grow in places that other crops won't. It was potatoes that allowed for rapid population growth in Ireland, and so when the famine occurred, it massively disputed the country's food supply.

In addition, it must be remembered that the British government's refusal to provide sufficient aid was a major factor in the famine being as deadly as it was. This refusal was motivated in large part by laissez-faire dogma; to quote one article on the topic:

“Ireland’s economy had always been made subservient to British interests,“ Quinnipiac University Professor Christine Kinealy says. “Following the appearance of the potato blight, a number of people in Ireland requested the government to close the Irish ports to keep food inside the country. [The British] refused to do so on the grounds that merchants would bring food in under free market forces. Of course, this did not happen."

I hope this sufficiently answers your question. Please let me know if there are any important factors that I have failed to address here.

The Irish were dependent on crops because of British colonialism. It's not that Ireland couldn't sustain other crops, but the era of British colonialism uprooted and decimated pre-existing Irish culinary traditions and all but unilaterally replaced the Irish diet with the potato. Yes, the potato is well suited to growing in Ireland, but it isn't native to Ireland (introduced around 1580s to 1600s, or relatively late, as you point out), and it largely became a method of social control that ensured British dominance by exporting all other food products (including wheat and other food we think or as Irish-- like salted meats). The potato was an effective tool of colonialism that kept the peasantry alive while saving as much land as possible for the British (absent) landowners, and allowed them to maximize their profits while maintaining the social order. The reliance on potatoes, which was largely imposed by the British, in turn became a way for the British to racialize and demonize the Irish as inferior beings with less sophisticated palates. This reliance and racialization imposed by the British is why the famine was so deadly. It wasn't just that they were reliant on the potato because of British rule, but that the British used their reliance to blame them and refuse aid, while insisting the market (which the Irish were excluded from and was run almost exclusively by prejudiced British merchants) would solve the problem.

Hasia Diner's Hungering for America has a pretty good chapter on the dominance of the potato in Ireland.