Quite simply, they don't. They average more than us at the moment because they have had their stadium move and we haven't. Before that time, they were averaging 15-17,000 at Roker Park. They also give loads of tickets away for free, have cheap deals for £10-£20 and their normal match tickets are about £25-£35 and aren't obstructed like 5,000 of our seats are.
Everton are 5th on the post war average home attendance list and have slowly over time been dismissed by neutrals who because we've been suffocated by a 22 year trophyless spell and an ageing stadium with limited capacity believe we are an also ran fanbase. Before City and the RS expanded recently, we were one of only 5 clubs who had averaged over 50,000 in a single season. We are 4th on the all time record attendance list and whilst the RS boast a record attendance of 61,000, we got 70,000+ crowds on many occasions. The RS' best crowd wouldn't even feature on this list and these are facts:
http://www.evertonresults.com/highallhomeatts.htm
When we get our Stadium move (and all being well some success with the Moshiri takeover) this country will see how big Everton are and how big our fanbase is. We will leave clubs like Sunderland, Villa, Leeds etc behind and will be back amongst the best attended teams in England.