Writing
Writing about yourself when you hate doing it

In short
The discomfort comes from trying to praise yourself, which is not what the document asks for. Report what happened, in specifics, and let the reader draw the conclusion. Evidence does the persuading that adjectives cannot, and it is far easier to write because it is just description.
A large share of the applicants I work with can talk for twenty minutes about a project and then freeze completely when asked to write two sentences about themselves.
It is not a writing problem. It is that they have been asked, as they understand it, to boast, and they were raised not to. The way out is to notice that the document never actually asked for that.
The instruction you think you were given
Tell us why you are excellent. That reading produces sentences like 'I am a highly motivated and dedicated individual with a passion for research', which are excruciating to write and worthless to read, and which every committee sees several hundred times a cycle.
The actual instruction is narrower: show us that this programme follows from what you have already done. That is a claim about a sequence of events, not about your character, and events are describable without self-praise.
Report, do not rate
The single change that unlocks most people is to stop assessing yourself and start reporting. Not 'I led the team effectively' but 'I rewrote the group's data pipeline in the last three weeks of the project because the original one silently dropped null rows'.
The second sentence contains no self-assessment at all. It is a description of something that happened. It is also far more persuasive, because the reader arrives at the judgement themselves and judgements people reach themselves are the ones they trust.
The interview trick, done alone
Say it out loud to somebody, or to a recording, before writing it. Almost everyone who cannot write a sentence about their own work can talk about it fluently, because talking about what you did is normal and writing a self-assessment is not.
Then transcribe and cut. The material that comes out of speech is nearly always more specific than the material that comes out of a blank document, and specificity is the thing you were struggling to produce.
What modesty costs you, and where it does not
Understatement is fine in tone and expensive in content. Writing 'I was involved in a small study' when you designed the protocol and ran the analysis is not humility, it is inaccuracy, and the reader has no way to recover what you removed.
The rule that keeps both: never inflate the claim, never shrink the facts. You can describe exactly what you did in a flat voice and still be the most convincing file in the pile.
When it is still not coming
Write the fit paragraph first. It is about the department rather than about you, so the resistance is lower, and having argued why this programme is the right one you will find the paragraphs about your preparation much easier, because now they have something to point at.
This is also why we do the programme research before the personal material rather than after. The order matters more than people expect.
Related questions
Is it wrong to sound humble in an SOP?
Tone can be as plain as you like. What cannot be humble is the content: if you did the work, say what the work was. Committees read a vague description as either a small contribution or an unwillingness to be specific, and neither helps you.
How do I write about work I did as part of a team?
Name the team's goal in one clause and your part in the rest. 'Our group built X; I was responsible for Y, which mattered because Z.' This is honest, it is standard, and it is much more informative than either claiming the whole project or disappearing into the we.
Should someone else write it for me if I find it this hard?
Getting help with the writing is normal. What matters is that every claim is yours and you could defend it if asked. If a finished document contains sentences you could not expand on in conversation, that is the problem to fix, whoever typed it.