Hard work: that is what people in a start-up often do. From the growth mindset they try to develop the company further. Usually, a team member automatically grows towards a certain role. However, not everyone can reinvent themselves all the time - and that's okay. Maybe they don't have what it takes, or don't have the energy to keep growing. It may mean that a colleague has to step aside or down, or that they have to say goodbye. It's always tough, but the key is to 1) accept that it happens and 2) continue to treat each other with respect. This way you make sure that the departure of one person does not slow down the whole company.
Honest is the best policy
However difficult it may be, as an entrepreneur you should always try to be honest when you are thinking about letting go of a team member. After all, it only becomes more difficult if you are not transparent. Here's an example. Suppose you have to let go of someone called Gus. Chances are he'll be angry at first, but if you're fair and give him a chance to find another job, he'll probably - at least in my experience - respect you. If you lie to yourself and Gus and don't cut the knot, you'll both be at a disadvantage. He'll be demotivated and/or insecure and may leave a mess behind, and you'll build up frustration because you know Gus won't function. Your relationship will come under pressure.
A relationship under pressure is no fun for anyone. Perhaps the most difficult is when you also have a friendship with a colleague who has to let you go. Let's call her Janine. How do you fire her? In my experience, this is also the best place to start the conversation openly, transparently and respectfully. If necessary, give Janine the opportunity to accept another position in the company and offer her a raise in salary. This is to thank her for her efforts, since she has brought you this far! The dismissal is not a punishment, because Janine hasn't done anything wrong - she's just not the right person in the right place anymore.
The most normal thing
It is quite normal that not everyone can keep up with the developments of a company, especially in a growing organisation with changing activities and responsibilities. You cannot expect that a colleague who first runs a 10-strong project himself, will of course be able to manage 100 people a few years later.
It is important to be honest about a person's suitability for a particular role, but as an entrepreneur, you should definitely invest time in the development of your team. I think you should always provide your employees with good feedback. In many companies you have a meeting every (half) year to do that; I am more in favour of giving feedback on a weekly or monthly basis. Say "I think you're doing a good job, but you can develop in this" and make room for feedback to you as well.
If someone leaves a company in a bad way, it is your fault as the founder/CEO. It is not your responsibility to make every individual grow with the organisation, but it is to run a company where the right people are in the right place. A start-up team is committed to the company together, to build something special and to benefit from it together. If an employee cannot keep up with the work, then you as CEO have not done your job properly. Among other things, you have to ensure that the work-life balance is in balance.
On good terms
So far, I have talked about the situation in which you, as an entrepreneur, have to let a colleague go. Of course, she or he may also want to say goodbye themselves. (If it is also painful in the long run, you are doing something wrong. My rule is: an employee who is indispensable should be fired first. That is not a healthy pressure for your team member, and the company should not be dependent on one person). Have respect for a colleague who leaves and be happy if she/he has found a nice new challenge. Of course it can be annoying if there is a gap in the organisation, but you get the chance to attract a new employee with different insights and perhaps more experience. This way, your start-up can continue to develop.
It is also possible that employees will come back to you, if you treat their departure with respect. This has happened several times with us. That is great: those colleagues return with new insights, as if they had travelled the world for three months. Moreover, it is of course a huge compliment for you and your company. They have had a taste of another organisation, but still prefer to work in yours. You can put that in your pocket!