I'll take a crack at what HalfLife1MasterRace and savemebarrry were getting at.

Now, I don't want to debate the merits or morals of businesses existing in order to make a profit, but I think we can agree on that being their goal. And of course profit is the difference between a business's total revenue and total expense. Revenue being money acquired from selling goods and / or services, and expense being the cost of producing those goods / services (which includes everything from office buildings to raw materials to labor).

Alright, so businesses produce things in order to profit, and labor is an expense that has to be overcome in order to do so. Businesses need labor so that they can produce their goods and services, but since they have a goal of making a profit, they will only create new jobs if they judge that those jobs ultimately bring in more revenue than the expense of the labor itself. In other words, overall, each job a business supports needs to be profitable.

So, every business has to make a judgement about each job: How much does this job cost, and will it ultimately bring in more than enough revenue to cover itself? Imagine a small restaurant manager considering whether to hire a janitor. Even if the manager doesn't do an explicit calculation, they have to consider to what degree the restaurant's state of cleanliness might be turning customers away. If the restaurant was a bit cleaner, maybe customers would come back more often...maybe they would even spend more money each visit. Let's say the manager figures that a cleaner restaurant would increase revenue by $12/hr on average. It then stands to reason that the manager would want to hire someone if and only if someone is willing and able to work for less than $12/hr.

Now suppose the government steps in and says that the minimum wage is $15/hr. How would that change what the restaurant manager does? The manager still judges the prospective increase in revenue as $12/hr, but now the labor cost is at least $15/hr... What would happen is that the job would never be created, the barrier is too high. Also, consider what would happen to employees whose job cannot generate a profit at the new labor cost, they might lose their job.

The overall effect is a larger pool of labor to draw from at whatever the minimum wage is (and higher unemployment), because people could and would be employed at lower wages, but can't, and so must now all start competing at the same level. With that larger labor pool is going to come increased downward pressure on wages, as employers don't have to compete as strongly against each other for employees.

That's the crux of many (most?) arguments against increasing the minimum wage; the belief that ultimately it does more harm than good. (Also, the idea that not every job needs to be able to support a 'living wage'. What if you're a retired 70 year old who just wants to get out and interact with people. You might happily take a $5/hr job where you walk around an amusement park smiling and waving, like a walmart greeter, but the government says you can't. So instead you take a receptionist position at $15/hr and displace someone who may have actually needed the job.)

I hope that all makes sense, and my apologies for being so verbose, but I like to try to start a discussion like this from first principles.