Along with the good answers by Joe W and Alexander The 1st, there's another pressure that's vocal, but less based on fact.
There are many people who are working low paying jobs and have college or other degrees beyond a simple high school diploma who are working for less than $15 or $20 an hour. Some of these people, unfortunately, apparently want to have the ego boost of holding their wages over someone else's head, as in they want to feel they are worth more than someone "flipping burgers". They believe that working in an "unskilled" job like that should warrant a much lower pay than they are getting.
These low paid employees, oftentimes in tech position or other office work, want to feel like they are worth more than the average restaurant employee, which they also usually consider to be one of, if not the lowest forms of employment. They make the argument that these restaurant employees should be making less than them, using various excuses that make very little real world logic.
Example: "I went to school for 4 years and am making $15 an hour, so why should someone who is still in high school make that much?"
This is while they are ignoring the fact that they are being severely underpaid themselves and that having the minimum wage increased would work heavily in their favor to get wage increases for their position.
The reality is that these low paid office workers should also be making higher wages. If the minimum wage is $15, they should be making at least $20-25, if not more. And if the minimum wage is $20, then they should easily be making $30-40. But the overly simplistic way they see the increase of the minimum wage doesn't allow them to understand this.
There's also the corporate world which has many people (even those not on the low pay end of the scale) convinced that businesses can't afford higher minimum wages. It's long been the rule of thumb to fire people to control spending to increase business profits, which employees fear would cause them to lose their jobs. This continues even during times when businesses report record quarterly profits (which also flows into increased inflation rates, but that's off topic here).
Along with that, the corporate world has somehow convinced workers that doubling the minimum wage will double the cost of having employees which will in turn double the price of products and services. That could only be true if all employees were paid minimum wage and if product & service prices were tied directly to the wages of employees.
Neither is actually true. This can be proven with simple logic. Management, especially C-suite level management, aren't paid minimum wage. In fact, CEOs are paid, on average, +300 times what their median paid workers are (not even the lowest paid workers). Also, products and services have been steadily increasing for over 40-60 years to be 10 times or more what they used to cost, while wages have only increased 2-3 times in that same time period. The prices of products and services are also dependent on the costs of travel/shipping, equipment, building rents/purchases, materials, and a whole bunch of other considerations.
The prices of products and services also depend on how much profit the business wants to extract from their customers. There's nothing inherently wrong with profit, but the corporate world wants you to believe that they are running on bare subsistence profits which just barely cover the cost of wage, while at the same time boast those record profits I mentioned earlier, as well as record profit sharing with their stakeholders, record bonuses and salaries for their CEOs, record amounts of stock buybacks, and other examples of how much money they make. Corporations are also laying off people as they boast record profits.
So, when you combine the egos of low paid employees and the fear of losing a job, there's a lot of push back against doubling the minimum wage. That fear is a huge part of why the "Fight for 15" hasn't already succeeded. And that fear is multiplied when instead of doubling the minimum wage, it's suggested we nearly triple it to $20.
Some of the opposition to the $15 or more minimum wage raise confirm most of what I said, especially about losing jobs.
The "Fight for 15" movement has started looking at $18-20 an hour, but has seen critics cite restaurant closures and other issues as relating directly to the increased pay rates.
Studies show that $15 an hour isn't a living wage, as reported last year, and while some people are fighting for higher minimum wages, they immediately get pushback about corporations laying off people and how it negatively affects business profits.
I've yet to find any article on reliable news media that states opposition to the minimum wage increase is due to egotism, but it's all over social media. When anyone talks about the increase, it's almost guaranteed to mention that "burger flippers" should be making less money than the posted does, even to the point where I've seen people saying that $7.25 is over paying these workers. When you get people to go on record they think people deserve to be paid less, they couch the jobs as "unskilled labor".