てくれる
te-kureru
Drop it and the grammar survives, but you sound cold
The picture What the other person did flies toward me like an arrow and lands. Gratitude rides in on that arrow. てくれる is the arrow coming to me; てあげる is the arrow leaving me for someone else.
Where the picture shows up in てくれる
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a kindness that reached me
友達が空港まで送ってくれました。
tomodachi ga kūkō made okutte kuremashita
A friend drove me to the airport.
I am in the passenger seat of my friend's car and the airport sign is coming up through the windscreen.
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teaching that stayed with me
先輩が仕事を教えてくれました。
senpai ga shigoto o oshiete kuremashita
A senior colleague taught me the job.
My senior's hand turns the document around to face me and taps down the steps one by one.
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asking for the arrow
ちょっと手伝ってくれない？
chotto tetsudatte kurenai?
Could you give me a hand for a second?
Hands full, I hold one out toward the other person and ask them to come this way.
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care aimed at me
医者が丁寧に説明してくれた。
isha ga teinei ni setsumei shite kureta
The doctor explained it to me carefully.
The doctor leans in toward me and draws a small diagram on paper while explaining.
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landing on my side of the line
母が弟に自転車を買ってくれた。
haha ga otōto ni jitensha o katte kureta
Mum bought my little brother a bike.
The bike Mum holds out goes to my little brother — and he is standing inside my side of the fence.
Even if I am not the receiver, family counts as my side, so くれる. To an outsider it would be あげる.
All of it in one picture
てくれる does not mean 'do for me'; it draws the direction the action travelled: toward me. My friend's car arrives with me in it, so the arrow lands in the passenger seat; my senior turns the paper to face me, so the teaching lands on my side. Holding out a hand is asking for the arrow to be fired this way; the doctor leaning in sends care down the same line. Even the bike handed to my brother counts, because he stands inside my fence. The gratitude comes along because the direction was drawn that way from the start.