If Buddhists do not kill, why do they eat meat?

I find many do not actually understand why Buddhists eat meat, even though our First Precept is on no-killing or non harm.

The difference is in the intention. If you go to a market or a restaurant, points at the fish and instruct it to be killed, then the seller takes and kills it, then you have broken the first precept of non killing. This is even though you did not kill the being yourself but had instructed someone to specifically kill that fish.
The reason is because the fish would not had died at that time (even though it may do so later) had it not been under your instruction.

Instead, if you go to the supermarket and buys a frozen fish, there is no precept broken as we did not ask for that fish to be killed. It had died earlier or probably a long time ago.

It's always with the intention.

Take the 5th Precept- for instance- No lying.
Now let's say that you are a mutual friend of a couple. The wife, who is your good friend, came to you with a confession that she'd had an affair with someone else but had terminated it. She felt bad and very guilty. After hearing about it, you felt it was very unfair to the husband, who is also your friend. So you went and told him about it- after all, it's the truth, right?
As the result of that, the couple had a big fight and the husband could not forgive his wife. Eventually, they divorced.
You may not have told a lie, but the truth had separated people. It is still 'wrong speech' and the intensity of the kamma committed will depend on your intention. If the intention is due to being vindictive, it will bear a more negative kammic effect.

Kamma exists- and ultimately, we have to bear the results of its fruition. I have seen so many instances of this with my own eyes. A friend of mine, who was used to slandering and speaking the truth that had separated people, is now facing the negative effect of that. As she matured, she stopped doing that but the effects of the past still haunts her. In the past, her speech had broken friendship or caused unfair judgement being placed on others. Now, she's accused of things that I knew she did not do. Yesterday she asked me why others kept blaming her of things or words she did not say.... as I listened, I recalled years ago on how she had done the same to others.

Back to killing fishes, I want to share with you a real life story. When I was in Thailand, I met this Ubasika (nun) who had practiced meditation for many years. She relayed to me an experience she'd had:

One day when she was meditating, an intense pain attacked her stomach. She felt her stomach was being slit apart. In deep concentration, she searches for a cause. And she met the spirit of a fish. She had slaughtered this fish many years ago when she was a layperson- she had caught it alive and slit its stomach. The spirit said: "I can still forgive if you kill me, but I am really hate you for killing my babies."

True enough, she remembered that when she had slit that particular fish, its stomach was filled with fish eggs. The fish was pregnant that time. As her meditation practice and precepts were strong, she sent merits to the spirit and asks for forgiveness. The spirit accepted the merits and were gone. And her pain disappeared.

If you read Ajahn Mun's Spiritual Biography written by Luangta, you will come across similar stories as well.

If we continue to question studies on a purely intellectual level and not through the heart, we will not be able to fully understand the Buddha's teachings. It's only by understanding the teachings from our heart, we understand the value of the precepts. We will know what is right and what is wrong cause the answers will come from our hearts.