I think most people are just offended by the almost automatic arrest of someone who acts in self defence. But this is really a procedural matter - it might seem really obvious that the person was acting in self defence, but the police cannot just make that assumption at the outset, especially in serious cases involving a death.
It's also a side effect of the creeping ideological position that if you are arrested you're probably guilty, and hence there is no reason to fund decent remand prisons, legal aid, and a justice system that can resolve cases in a timely manner. That attitude's all fine until someone who is probably a victim gets sucked into the justice system and it becomes apparent how your punishment begins long before you ever make it to trial.
As a UK resident trained in self defence, being arrested as a matter of procedure is a good thing and were I ever in a situation where I had to defend myself I'd happily go along with it. Being "arrested" is a bit of a misnomer because it conjures up images of being dragged off in chains by a sneering bobby where as in reality it's more of a "Sir, we need you to come to the station with us to make an official statement". Being arrested does not mean you're automatically charged with anything, when you stop reading the Daily Mail you'll quickly find out that most people aren't even charged because the self defence, defence is so bleeding obvious it's just not worth anyone's time.
There are two main reasons and one minor one why I'd completely co-operate with the Rozzers if I ever had to violently defend myself.
1. I'll be pretty badly shaken up and you'd be completely retarded if you weren't. I'd likely have a minor injury as well. Cops in the UK will have someone at the station trained to help you or at the very least offer you a cup of tea.
2. It lets me get my story straight (as an act of self defence) from the very start and very much on the record. If it ever goes to court, this is a huge advantage for anyone claiming self defence. Conversely if I didn't co-operate with the police it would look quite bad in the eyes of a judge or possibly even a jury.
And the minor one.
3. Whoever I beat up or harm might come back with a few mates looking for payback, I'd rather not be there if they do.
The actual law on self defence in the United Kingdom is considerably less alarmist than the tabloids would have you believe. https://www.cps.gov.uk/legal-guidance/self-defence-and-prevention-crime. The other big misconception is "reasonable force == no more force than absolutely necessary" where as in reality the law understands that under such a stressful situation people cannot be relied upon to know exactly how much force to apply, so there's a lot of leeway, the excessive force clause is only there for things that are very, very egregious (I.E. striking them a few times unnecessarily is not considered excessive, taking them outside for a curbstomp is). Generally the only "gotcha" is if the perp is trying to escape, let them. Don't chase after them. If you do then it's two counts of assault and you only get to claim self defence for one.