Other users' coins instead my own?

Question

I found some advices about anonymity, however one sentence is unclear for me

The quote comes from https://en.bitcoin.it/wiki/Anonymity

The protection that this method offers is significantly reduced if you are trying to anonymize more than about 10% of the total number of Bitcoins that the eWallet service holds. You'll end up getting your own coins back instead of other users' coins. Withdrawing Bitcoins more slowly and in smaller increments will help reduce this problem. Sending coins to an eWallet service in the largest single transfer possible will also help.

I don't get idea of "your own coins" - as far as I know there is no "coin" as an identifiable whole, just a log of transactions which balances as ones "bitcoins amount". What was the author intent to express by this sentence?

Answer 1

Yes, you are right. There are no "coins". There is only an ability to write some data (transactions) into one global file (blockchain).

But it is possible sometimes to track who is an author of transaction. For example, I am buying something in online shop (with delivery) and paying bitcoins for it. Now the shop knows my name and my address (for postage). The spending transaction has a "change address". If I use the same address for change - the shop owner would also know (with some probability) the amount of bitcoins in my wallet! Some people may think that this is not good, especially if they have large amount of funds.