This is something I wrote a little while ago for a children's anthology in which friendship was one of the themes. It might provide a starting point for some writing on the subject.

A friend is someone who borrows your ball
And returns it to you later in the day,
Who will lend their newest pens - and will play
Your games. Who'll come round to your house and call
For you in rain as well as when it's fine,
Who'll listen to your secrets, share your fears,
Lend a shoulder when your eyes are full of tears
...And won't divide things into "Yours" and "Mine".
A friend will peel the plaster gently off your cut
And won't say "Yuk!". A friend laughs at your jokes
When everyone else goes "Eh?"; who likes you but
Will tell you when you're wrong; who strokes
Your favourite pet in spite of all the fleas;
Who knows you well - and when invited, still says, "Yes please!"

Education...

We were
two pooh sticks
in the same stream
bobbing along together
till we separated into different rivulets:
the science and the arts
and discharged into a vast
sea of sticks, driftwood, branches...
I wonder where he is now.

Some changes at the beginning in addition to the tweaks I mentioned last time.

Education...

...in the A stream
two pooh sticks
bobbing along together
till separated into different rivulets
the science and the arts
and discharged into a vast
sea of sticks, driftwood, branches...

In the A stream sounds a bit of a show-off, though it's reminiscent of the A team, for those who remember it.   Perhaps just 'in the same stream'.
'Till we separated' might give less of an impression of things being out of our hands. We didn't have much choice but at least we could decide (or rather had to decide) between arts and science.  What would da Vinci have chosen?  No place for Renaissance Man at Woking Grammar School! 

In the A stream
Two pooh sticks
rubbing along together

bobbing along?  what do sticks do when they're going downstream?

till separated into different streams - no, not streams again - rivulets perhaps.

In the A stream
two pooh sticks
bobbing along together
till separated into different rivulets
the science and the arts
and discharged into a vast sea of sticks, driftwood, branches...

Of course the image gives the impression that we were entirely subject to events, which was not the case.  So the image doesn't work all the way.

When I made it to Grammar school I felt out of my depth - socially, at least. Boys only, of course, and seemingly all from well-off families with cars. I became friends with a quiet lad called Roger Speed. I wonder what became of him. Already streamed off from our secondary modern companions, we were now channelled into an 'A' stream which swept us on towards further waterfalls, weirs and eddies before discharging us with a great splash of speech days into the world of work or university.  Unlike a river, growing as tributaries join it, this stream divided into smaller rivulets like a brnaching delta. At 14 we washed into arts or sciences and at sixteen into A levels or the sea. At one of those divisions (arts / science) Speed and I were off on our separate ways.  (And yes, we never called each other by our first names. It was either surname, or nickname.)

In the A stream
Two pooh sticks
rubbing along together

is at least a start.

My memories of school suggest that friends are different at different ages. Often one's friends were really acquaintances and frequently the result of having to sit next to someone.  Not having anyone in particular to sit beside was an embarrassment although it did lead to new 'friendships' sometimes. Seating arrangements in schools have changed, at least in primary, but even at tables or in groups there must be a pressure to have a person who is your friend.  In secondary schools two-person tables still seem to be the default seating plan. 

Friends were also more fluid - though I speak as a boy and maybe it was and is different for girls. Your friend at playtime might be different from your friend playing football or in a particular lesson.  Only later  - say upper secondary - did friendships begin to form which were more like the ones which I know now.

As I think about this I begin to have an image of things forming and reforming. Ships that pass? Amoeba linking and separating? Clouds in the sky?  The right image might give me the piece of grit around which to grow my oyster.

As I finally put 'Autumn' into the archive I realised that there was another 'Autumn' there - from 2008!  When I had a look, I saw that I'd had quite a lot of trouble with the theme last time - though the outcome as well as the process was quite different. 

The difficulties I had should be a reminder to us all when we expect pupils to write to order.

However, I now have to write to order as an anthologiser has requested poems on the subject of friendship. I do have some poems on that theme which I'll look out but I'd like to submit something new too.

As with autumn, the problem is to find an aproach which is not hackneyed.