This is a really common question, mostly because the dairy industry works very hard to make people think exactly that, despite their better judgement. I was in the exact same position as you not so long ago, I was a happy, proud vegetarian and I believed that milk and eggs were not cruel.
The truth is, like all mammals, cows only produce milk when they are pregnant. They produce it for their calves, not for us. In order to produce milk, every dairy cow, on every farm has to be forcibly inseminated. She will have bull semen forced into her vagina by a farmer’s hand, or sometimes using a bear-claw or machine. When her calf is born, if that calf is a female she will join the milk production line like her mother, if he is male then often he will be shot at birth, or sent for veal production. At the very least the cow must be separated from her calf so that you can have her milk. The truth is, for every sip of milk you are drinking, there is a calf who is not. Cows form close emotional bonds with their calves, and separating them causes extreme distress, many dairy workers and animal activists have written testimonials describing the horrific noise mother cows make when their children are taken from them.
The vast majority of milk does not come from cows in fields as the packaging and adverts would have us believe, most of these cows will have been born, and will die, in crowded, intensive milk production facilities where they are hooked up to huge machines that suck their udders dry. These machines also cause diseases like mastitis, which is extremely painful, and is responsible for the not insignificant amount of puss found in commercial milk. Cows have about three or four children taken from them until their bodies are so spent that they simply cannot produce anymore milk, at which point they too, are killed. Between 20 and 40 percent of hamburger meat comes from dairy cows, dairy and meat is inextricably linked. I would honestly say that without a doubt, there is more cruelty in a glass of milk than in any other animal product, including meat.
Milk is not only cruel, it is environmentally destructive and wholly unnecessary. No other species on the planet drinks the breast milk of another species, and we don’t need cows milk anymore than we need elephant milk for a healthy diet. You’ve made a great step by being vegetarian, but in order to fully follow through on those values, and to not be selective in your compassion, you just have to take it the whole way. Otherwise, you are still paying for animals to die, and they are still suffering on your behalf. It is one of the most difficult truths I have ever had to accept, but it is true nonetheless. Milk is not ours to drink because animals are not ours to use; not for their flesh, their skin or for their bodily excretions.