The IRA proclaimed itself "the lawful and legal" government of Ireland,why does it reject the standards and responsibilities of a moderngovernment?

The IRA Green Book was in existence while the IRA, (1956 edition), and the PIRA, (1977 edition) waged their armed stuggle. The Green Book said:

"Commitment to the Republican Movement is the firm belief that its struggle both military and political is morally justified, that war is morally justified and that the Army is the direct representative of the 1918 Dail Eireann Parliament, and that as such they are the legal and lawful government of the Irish Republic, which has the moral right to pass laws for, and to claim jurisdiction over the territory, air space, mineral resources, means of production, distribution and exchange and all of its people regardless of creed or loyalty."

IRA cling to notion of themselves as a platonic government of a non-existent republic. The IRA "creation myth" was explained by Michael McDowell in the Irish Times in August 2015:

"To understand what is going on at the moment, one has to understand the IRA “creation myth”. The IRA Bible, otherwise known as the Little Green Book, asserts that the IRA’s Army Council was, in 1938, formally and in writing handed over the role of the “Government of the Irish Republic”, established in 1916, by a handful of irredentist opponents of the Treaty who had been members of the Second Dáil up to the ratification of the Treaty in 1921. 

These former TDs somehow convinced themselves that even though most of them stood in subsequent elections to Dáil Éireann (some of them were defeated and some of them were elected), the body to which they sought election was a bogus, usurper parliament without legitimacy."

When the provisional IRA was formed in 1969, it immediately sought recognition as the legitimate inheritors of the Irish Republic from Thomas Maguire, the last surviving member of the Second Dail. Maguire duly "gave” them the Republic. Thomas Maguire, the last surviving member of the second Dail, said:

"I recognise no Army Council or any such body that advocates participation in the usurping legislature of Leinster House."

Fintan O'Toole said:

"The IRA saw itself as the true government of Ireland and its own internal regulations as better law than any passed by the Dáil or enforced by the Garda."

He also wrote an article in February 1998, 'The End of The Troubles?' In that he explained support for IRA and the electoral success of Sinn Fein during the Troubles:

"The most obvious was that between the IRA’s claim to act on behalf of “the Irish people” and the fact that, when it began to vigorously contest elections in the Republic of Ireland after 1986, it received less than 2 percent of the vote."

Fintan O'Toole continued:

"The IRA traditionalists had pointed out with irrefutable logic that engagement in democratic politics undermined the supposed moral validity of armed struggle. One of the most telling remarks in Peter Taylor’s book is made by the veteran Belfast IRA leader Billy McKee: “If you recognize [the Dublin authorities] as a government, you must fall in line with them. You’ve no authority to take a life. Then it would be murder.” The abject failure of Sinn Fein to win any kind of democratic mandate for the IRA’s violence stripped away the rhetoric of republicanism and exposed the murderous nature of its campaign." 

Newton Emerson said:

"Writing exclusively for the Irish News on the victims issue, secretary of state Theresa Villiers said the British government has been “far more open than any of the paramilitary groups that operated during the Troubles.” 

While this may be true, it glides over the point that paramilitary groups are not the yardstick by which a government’s conduct should be judged. 

However, neither Sinn Fein nor its proxies can make this point, as their entire world-view is premised on equating a paramilitary group with a government. So both sides are deadlocked in qualified silence, which is exactly how they like it."

On the matter of the murder of Jean McConville, Mitchell McLaughlin said when asked whether he classified the shooting of Jean McConville, a mother of 10, as a crime:

"I think it was wrong."

Asked again whether he thought it was a crime, he replied:

"No, I do not."

The Sinn Fein member also agreed with a remark that the IRA was "the only legitimate government of Ireland". The Irish Justice Minister Mr McDowell said in response:

"Mitchel McLaughlin and his colleagues believe that any volunteer carrying out any authorised action on behalf of the IRA does not commit a crime because the IRA is the legitimate government of this country. That is what they all believe and that is why shooting Jean McConville, this poor woman, in the head is not a crime in your book because it was authorised by a court martial of the IRA."

Fianna Fáil TD, Mr Brendan Smith said:

"It is the Irish people, not the IRA, who decide who governs Ireland... It is disgusting for Sinn Féin to suggest a backroom cabal are this country’s legitimate government."

Fintan O'Toole wrote that the worst thing you can do to your opponent is to preserve your own better values. wrote in the Irish Times:

"[What makes] Borstal Boy so fascinating and so important… If you read the book carefully, what emerges is a remarkable story about the worst thing you can do to a terrorist. It is not to execute him or to waterboard him or to render him to Guantánamo. It is not to tear up democratic ideals. It is to preserve your own better values. This is what happens to Behan: the evil Brits deprive him of the glory of martyrdom by treating him remarkably well."

And finished:

"In some ways Borstal Boy is Behan’s The Hostage in reverse. In that play a young English soldier is held hostage by the IRA and a mutual affection develops in spite of everything. In Borstal Boy the same things happens, but it is to Behan himself. There is, though, one huge difference. In The Hostage the IRA kill their prisoner anyway. In Borstal Boy they simply kill his fanaticism with kindness."