McAnespie was born into a Catholic family in Aughnacloy, County Tyrone, Northern Ireland, a small town with a Protestant majority. He was raised by his grandmother from the age of 3; she died a month before him. He was a member of Aghaloo O'Neills Gaelic football club. McAnespie grew up with segregated schools and sports teams amid extreme tension between the Protestant and Catholic populations. Many young Catholics in town reportedly were encouraged to move to America, Australia and even England because of harassment from Unionists. "They say things like 'Got any bombs today?'" reported one of McAnespie's teammates, Seamus Singleton, shortly after his death. A Catholic priest, Rev. Joe McVeigh, stated that sons from large families were especially targeted for harassment in the hope they would encourage their families to leave.
At age 16, McAnespie finished school and got a job across the border at a poultry plant in Monaghan, Republic of Ireland. He eventually became a foreman, despite the daily border crossings over the River Blackwater that reportedly involved intensive searches. The harassment against McAnespie reportedly intensified after his sister Eilish McAnespie McCabe decided to run for the Tyrone County Council as a Sinn Féin candidate. McAnespie was an election worker for Sinn Féin, but both the Provisional Irish Republican Army and his priest said that he was not involved in any paramilitary activity.
McAnespie was travelling to a match when he was killed by a gunshot wound to the back. He had just walked past a British Army checkpoint. The British Army said that McAnespie had been hit when the weapon had discharged accidentally as a soldier was moving the gun with wet hands. Forensic evidence suggested that the fatal shot was one of three that had ricocheted off the road two metres behind McAnespie.
Charges were initially brought against Grenadier Guard David Jonathan Holden for manslaughter but were dropped prior to prosecution. He was fined for negligent discharge of the weapon and in 1990 was given a medical discharge.
McAnespie's family allege a cover-up by the British government and question the likelihood of accidental discharge murdering their son from a distance of 300 metres. His father, in an article in the Observer Magazine, claimed that a soldier had stopped him some fifteen months before the shooting and told him, "I've a bullet here in the gun for your son Aidan".
The day after the killing, the Irish Government appointed Garda Deputy Commissioner Eugene Crowley to investigate the incident. The results of the investigation were received by the Minister for Justice, Equality and Law Reform Gerry Collins on 8 April 1988, but have never been published. A Royal Ulster Constabulary investigation took place which concluded that the killing was accidental.
In June 2008, the Police Service of Northern Ireland (PSNI) Historical Enquiries Team published its findings on the case. The report called the soldier's explanation for the killing the "least likely version" of what happened. The British Ministry of Defence said it had co-operated with the inquiry and understood that this did not uncover any new evidence that would warrant further investigation.
In October 2008, the PSNI investigation concluded that Jonathan Holden's gun required 9 lbs of pressure to pull the trigger, and that the soldier's account of the events was highly unlikely. It described the chances of this occurring, combined with hitting McAnespie by accident as, "so remote as to be virtually disregarded".
In June 2018, it was announced that a soldier is to be charged with manslaughter by gross negligence over the 1988 killing.
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