Why do we use the word cull?
Have you ever heard the word cull used in Numismatics? Whenever we hear a dealer use the word cull, it means that a coin is damaged or has some other market defect that excludes it from any grade.
Cull specifically means: to select from a group, reduce the size of the herd, or to hunt or kill.
So how did we get from that definition to it meaning a damaged coin?
The lowest grade a coin can get by third-party grading companies is PO1. When you get a chance search on eBay for coins graded PO1. There are many examples, but something almost all of them have in common is that they are priced higher than coins in Good through AU (G4-AU58). How does that make any sense? Here is a real example for sale on eBay right now.
1882-S PCGS PO1 CAC. Asking $450. 
In today’s market, an 1882-S would have to be in grade 66 to command that price.
And looks like this. 
Why would anyone do that? The reason is that it’s actually rarer for a coin to wear so far down and not become cull than to stay in MS65 Condition. It is kind of counterintuitive so stay with me. Imagine if that worn dollar could tell you the places it’s been. Coins do not get like that by sitting around. They get like that by being used. So, for that coin to have stayed in circulation for so long and not be damaged in any way (just good old fashioned wear) is quite amazing because if you think about it, it was never harshly cleaned, dropped, altered, holed, polished, dipped, or otherwise removed from circulation in its whole life. In other words, it never became a cull.
Our use of the word cull comes from a time when banks and just about anyone who took change, took the responsibility seriously to remove damaged coins from circulation. The bad or damaged coins were culled from the population and were often returned to the mint to be remelted and recast into newer coins. Damaged coins were always viewed with suspect in marketplace, as filing, clipping and a whole host of other ingenious methods to help lighten a coin of some its precious metals content. These coins were culled from circulation because they could not be trusted. And that’s why today we call damaged coins cull.