The excuses
Airlines refuse a large share of valid claims the first time. The refusals cluster around a few phrases.
"Extraordinary circumstances." The legal exception. It covers things genuinely outside the airline's control: severe weather at the airport, air traffic control restrictions, security incidents, political instability. It does not cover technical faults with the aircraft (the Court of Appeal settled that in Huzar v Jet2.com in 2014), crew sickness, crew running out of hours, or the aircraft arriving late from a previous flight. If the refusal says "technical issue" or "operational reasons", it is wrong in law.
"The delay was under three hours." Check your arrival time against the scheduled arrival time, at the gate. Airlines sometimes quote the runway time, which is earlier.
"You accepted a voucher." A voucher offered at the airport is not compensation unless you signed something agreeing it was. Most people didn't.
"You need to claim within [short period]." There is no such rule; see the time limits above.