iMac SD reader does not write or format or delete data - it only reads

Have you checked the position of the write lock switch on the SD card? It's possible that when you are inserting it into the mac it's being switched on.

http://kb.sandisk.com/app/answers/detail/a_id/1102/~/memory-card-is-write-protected-or-locked

 

This is a common problem through the range of Macs I am using (iMac 2009, iMac 2011, MBP 2010 and MBP 2011). It really is a big pain. I have no idea what is really going on either. Normally it works when I put the write lock switch in the middle. There are tons of People in the Apple forums who are experiencing similar problems. I really wish Apple will sort that out in future Macs.

 

What format is the card in?

 

Faulty iMac card reader

I have the same problem on my iMac (Intel 21.5"). Most likely it is a problem with your iMac's SD card reader.

Shine a strong light into your Mac's SD card reader: you will be able to see a tiny, brass-coloured latch on the narrow floor of the slot. If your iMac has the same problem as mine, then that latch will be sitting in the 'down' position (ie inserting the SD card does nothing to change its position).

Normally the latch sits in the 'up' position and is depressed when an SD card is inserted. With an unlocked SD card, there is a minuscule space for the latch to pop back into the 'up' position. With a locked SD card, the slider on the card blocks that minuscule space, thus telling the computer that the SD card is in locked position.

It seems to be a common problem (judging by the number of internet posts describing exactly your problem) with the iMac that that latch, after some usage, when depressed eventually fails to return to the 'up' position and remains instead sitting in the 'down' position, thus telling the computer every SD card you insert is locked, regardless of whether the card itself is locked or unlocked.

Why am i making this guess? Because i (and you) have tried the same SD card on an external reader and, in that case, the computer reads the card as (correctly) unlocked. The iMac card reader perpetually reads it as locked.

Solution? Apple may replace your card reader if your computer is still under warranty. Les-inconvenient solution: use an external card reader.