Most people assume it is natural and harmless to consume milk products. But if we take the time to get informed on this topic in a more detailed way, we will understand that the situation of a milking cow is worse than that of other livestock animals.

The word 'mammal' derives from the fact that a mother supplies her offspring with milk from her teats. The milk is produced until the young animal is capable of eating solid food. When it stops sucking regularly, the milk production slowly ceases. https://en.wikipedia.org/wiki/Mammal

In contrast to widespread belief this is the same with cows. That is why they are artificially inseminated every year, exactly at the moment when their milk production is bound to end. Thus a cow is pregnant nearly all her life so she never stops giving milk. The aim of farmers is to make as much profit – or milk – with a cow as possible. 

http://www.peta.org/living/food/thats-dont-drink-milk/ 

Leaving the baby cow with its mother would not be economically profitable at all. On the contrary: The calf would drink its mother's milk, which is supposed to be sold to humans after all. After two days as a rule, the calves are torn away from their mothers, put into calf boxes and exposed to red light. They are fed with cheap surrogate milk. 

In case it is a female calf, it will usually be used as a milking cow in its later life. It will be isolated, put into a calf box, where it will be raised and two years later, after the first artificial insemination, it will give milk for the first time. 

Male calves instead, are not really useful as they have no udder. They are not even suited for meat production as they possess the genes of a high-performance milking cow. This is why they are made into liver sausage, which is highly cherished in Germany, or into veal escalope. Sometimes they are even killed immediately after birth, which however is denied by the German farmers' association.

Few people know that many cows are slaughtered when they are pregnant. So every year around 500,000 cows die together with their calves in American slaughterhouses. While the mother cow is sedated (in 70% of the cases at best), the unborn calf suffocates miserably in its mother's womb. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3618883/

The circle of violation and child abduction is ended – we could say for the good of the cow – after four years as a rule. For after a certain time, a cow does no longer give enough milk to be profitable for the farmer. 

As if the suffering of milking cows was not big enough yet, the milking is often a painful procedure, too. Today's cows are bred to suffer. When, in 1950, a cow's annual milk yield was around 6,000 liters, it is around 10,000 liters today. Thus a cow yields up to 30 liters a day. Its udders are filled to bursting but the cow is only milked twice a day. A calf would drink several times, so the pressure and the tension would be reduced. Even milking can be very painful if the milking machine is not correctly attached.

Another issue is that many cows are kept on slatted floors standing in their excrements. This often causes diseases of the hooves. Besides, the build of cows has not adjusted itself to the ten times higher milk yield during the last 100 years, which among other things can provoke deregulations of their spinal columns.  Additional problems are infections of the big udders (mastitis, cf. photo), which are treated with antibiotics, which in return penetrate into the milk. 

https://en.wikipedia.org/wiki/Mastitis_in_dairy_cattle 

As the cow's organism is not made for this enormous output of milk, the cow is fed with concentrated feedstuffs. However, even these cannot provide the necessary amount of nutrients for 30 liters of milk a day, which leads to a constant withdrawal of nutrients from the animal's organism. The consequence of the lack of nutrients can be rumen acidosis and other metabolic diseases. The lack of calcium increasingly exhausts the cow's body. 

It has already been mentioned that after four years cows are unable to give enough milk any longer to be profitable. So they end up in the slaughterhouse where the ultimate profit can be made of them. If a cow yields less than 7,000 liters a year during the period of lactation (the time when most milk is produced) it is usually slaughtered earlier. 

This is a very questionable way of compensating her lifelong abuse, which has inflicted unimaginable physical and mental pain on it.

Furthermore most cows are kept in tie-stall farms, which means they stand in a space of 2 square meters for their whole life. In Europe, between 20% (lowland) and 80% (upland) of cows are tethered at least during the winter. Research papers show that approximately 88% of Norwegian dairy cattle, 75% of all Swedish dairy herds and more than one third of German dairy cows are kept in tie-stall housing systems, often without pasturing. According to the 2007 USDA report 62% of US dairy farms had tie-stall barns.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3674972/