The enforcement of this rule for small private sales is very light, and typically needs significant transgression before TS get interested (but of course there is always the exception!).
It is a particularly puzzling rule when you first come across it.
Abattoir -> Butcher -> public = legal
Abattoir -> Cutting plant -> you -> public = legal
Abattoir -> Butcher -> you -> public = illegal
So where is the risk in the last one that isn't present in the first two? ie if butcher is ok, and you're ok, where does butcher to you ADD any further risk.
Clearly not the butcher, as he's allowed to sell direct to the public, so if his processes were risky, adding you into the chain does not make it worse or better, he is already selling to the public. Clearly you are not the risk in itself, as a cutting plant can give you the meat to sell to the public.
The answer lies in volume. The State does not want qualified butchers creating large "chop shops" without the state ensuring that they are cutting without risk. The argument is the larger the operation, the more supervision is needed across the whole plant, and the more the state should be there to oversee it. If for instance you had 10 butchers of the same size in 10 different shops and one had poor processes, only a tenth of the public buying from them would be ill. If you had one large butchery of 10 butchers, the poor processes of one would infect all, and all their customers would be affected. You may or may not agree or like the state interfering thus, but that is how it is.
Allowing butchers to cut for people to sell on (ie become wholesalers) allows them to get bigger quicker, hence the reason for the rule.
The "derogation" quoted by lachlanandmarcus doesn't exist, but many TS take a view that whilst selling "privately" to family and friends does constitute a "placing on the market" it does not constitute a "public" sale - a public sale being considered as one where you may not know each buyer eg one where you turn up at a market stall, have a sign on your gate, or advertise.
Simply moving meat from you to granny is not something that many TS's consider as needing their heavy hands, but if they have had a bad day or argument with 'er indoors, they can still be a pain, hence why PP's butcher is saying that him cutting for you as customer is perfectly legal, what you do with it afterwards is your affair and he doesn't want to know.
However if you're advertising, or going to farmers markets, the cutting plant route is a better option to stay well within the law.