Why was the "Dispatch Reliability" of the A320 "low" during its first years?
The A320 saw entry into service on 18 April 1988 with Air France.
About a year later Flight International covered the dispatch topic. For British Airways – whose initial acquisition of the A320 was through the British Caledonian takeover, and not an order – the problems weren't with the plane, but with the Boeing culture that had to adapt.
Otherwise there was nothing notable.

(...) The &quot;culture difference&quot;, says Bracken, materialised in apparently trifling (but actually problematic) ways, such as line mechanics having trouble with Airbus literature. There was nothing wrong with the literature, it was just different.
November 1 came. &quot;It wasn't a very good start,&quot; says Bracken, &quot;but the reasons were outside the aircraft.&quot; By January, BA's A320 technical dispatch rate had not climbed out of the 96 per cent range, reveals Barry Gosnold, chief engineer technical services.
That is a revealing figure. BA had expected much more, even though the performance is not unusual for a completely new aircraft.The A320's performance with Air Inter at the same time was between 2 and 3 percentage points better, although Air Inter had received its first A320 months later than BA.

Source: AIRBUS A320 AT WORK, Flight International, 17 June 1989