The sensibility is like this I guess:
I am guessing that your family is vegetarian and the taboo of meat has been indoctrinated into you since childhood. When you see a crop of say, wheat, you see food. Because that is what it's purpose is and that's what you have known since childhood. However, you do not think that the Wheat is perhaps a wild plant that man somehow managed to turn into food. That was perhaps not its purpose but man gave it that purpose and systematically slaughters a field full of crops for human consumption. Same with livestock, man gave it the purpose as food and systematically grows and slaughters them for consumption. Only because its taboo in your point of view doesn't mean that its any different than consuming vegetables. A carrot a root, a pea is a seed, these die when you rip them from the ground and chop and boil and fry them. However, you take these facts for granted since you do not see it that way. If you see things from our perspective, you would perhaps see different.