When your chain stretches beyond a certain point and does not get replaced it will begin to wear down your gear teeth due to excess friction against the sides. Eventually your gears can become worn enough that they will cause skipping (aka chain slipping off the teeth).
This used to be common advice (replace the chain and cassette at the same time). Nowadays, the best pracrice is to replace the chain before it stretches too much and starts wearing down the cogs. If you do that consistently, a cassette should last a really long time. I ride about 2,000 miles a year commuting and have been using the same cassette for 7 years, changing chains about every other year.
Chains stretch over time and use. Oil them well and often and they last longer.
Measure your chain with an old style American ruler (with 'inches'). Twenty links should be exactly 10 'inches'. [0] If it's 1/8" 'inch' longer, replace the chain. If it's 3/16 'inch' longer, replace the rear cogs and the chain both. Consider replacing the front chain rings, too, especially if the chain is longer or they're made of aluminium.
A stretched chain ruins gears. Ruined gears will ruin a new chain, too. Proper maintenance fixes both problems. New quality chains cost about US$10-15.
[0] Wikipedia says one 'inch' is 2.54 centimeters, if you believe that.
Sounds like me - the middle gears on my DuraAce cassette finally wore out after 20+ years so I pieced together a new one. It's a major pain on vintage bikes, definitely want to change your chain before it wears and maybe get a higher quality chain. I also recently invested in a chain cleaner - loads of fun.
> I don't know who sold you a new cassette when you got your chain changed, but they are nothing but a salesman.
My most recent experience with new-chain/old-cluster was that the chain skipped a tooth three times per pedal revolution! Replaced gears, problem solved.
To go buy the new gears, I first had to temporarily put back the old chain, to make the bike ridable. :)
Adjusting the derailleur can help; in particular the "B tension" adjustment to get the jockey wheel to track the gear cluster more closely for more wrap. However, if it's that bad, it won't help.
I have decent experience adjusting derailleurs. Even taking apart the non-adjustable ones and drilling holes in new places to change spring tensions.
> 8-20 of them
You're not going to get 8 teeth of contact on an 11 tooth cog, nor 20 teeth of contact on a 26 tooth ring.
Yes and no. You will get slipping on heavily worn cassette (read: sawtooth shaped teeth) and a new chain or vice versa, but heavily worn these days might be 4-6000 miles of abusive riding. For the average commuter, this would be several years of use, as well as a fair deal of casual riding.
I stand corrected. I've never had that happen before but i'll take your word for it.
I still wouldn't consider a cassette something you should change as a matter of regular maintenance. Certainly not as often as a chain. I've had cassettes last through multiple wheelsets.
I recently had to replace my front chainrings after about 7000 km because the chain was jumping when I applied lots of pressure. The rear cassette was also replaced because the old chain (5k km) had damaged the cogs. So gears do indeed wear out, but it takes a good amount of riding.
That's just abuse. I ride much more than 7000km per annum and never change gears. Also, it's the worn chain that wears down the gears; replace the chain more often the the gears will last many years.
I've never heard of chains slipping teeth, most notably because it would need to slip all teeth in contact at once (8-20 of them).
If you are having your chain slip off, you need to adjust your deraileur.