Theory:

I quarrelled with my brother
I don’t know what about,
One thing led to another
And somehow we fell out.
The start of it was slight,
The end of it was strong,
He said he was right,
I knew he was wrong!
Explanation:
 
Most of us are born with siblings, big or little, boy or girl. Those born with brothers or sisters in the family know very well that just like sharing, having fun and loving each other's company, fights are also an essential part of sibling life. Any family where sibling rivalry doesn't happen cannot be a normal family because just like variety is the spice of life, fighting with brothers and sisters is the spice of childhood.
 
angry guy.jpeg
Our minds go to this mode whenever we quarrel (Image for illustrative purpose only)
  
As already mentioned in about the poet, Eleanor Farjeon had a childhood where she didn't have a lot of chance to interact with others because of her poor eyesight. She had spent most of her time with books and the only other way to pass the time when she was young would have been to play with her brothers. She describes one such incident where a fight broke out between herself and one of her brothers in "The Quarrel".   
 
siblings fighting.jpeg
Sibling rivalry begins here (Image for illustrative purpose only)
  
In line \(1\), she jumps straight into the story by plainly saying "I quarrelled with my brother" which tells us the situation in a single line, that she and her brother had not agreed on something and that had started a fight between them. Lines \(2\) to \(8\) go on to describe how the little quarrel had escalated quickly into a big fight. For example, in line \(2\), Eleanor says that although the fight had started between her brother and herself, she did not remember the reason behind it.
  
Lines \(3\), \(4\), \(5\) and \(6\) continue telling us how quickly a quarrel can grow in size as she says that one thing led to another and somehow they fell out. The words "One thing led to another" in line \(3\) tells us how quickly a fight can become big and not much attention is given to what had happened, but only on how fast things are going out of control. Here the words "fell out" in line \(4\) is very interesting because it is not both brother and sister falling out of the door or window hurting themselves, but they "fell out" because both of them thought that what they had thought was right and that the other person was wrong. Lines \(5\) and \(6\) continue to tell us how a strong fight can grow so quickly out of the simplest of reasons, and no real reason is needed for a quarrel to happen as the poet already tells us that she had forgotten the reason for the argument (line \(2\)).
 
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When disagreements happen, fights break out (Image for illustrative purpose only)
  
In line \(7\), Eleanor tells us that her brother said that he was right, but in line \(8\), she also tells us that she knew that he was wrong. This shows that in that moment of anger Eleanor gives more weight to her feelings than her brother's by using the verb 'knew' showing that she not only said but completely believed that her brother was wrong. This shows how we fiercely defend our side of an argument when we are angry while not at all caring about other people's thoughts on the matter.
 
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When fights break out, fall-outs happen (Image for illustrative purpose only)
  
Meanings of difficult words:
 
No.WordMeaning
1
Sibling rivalryFights happening between brother and sisters of the same family.
2
CompanyThe presence of others around a person.
3
To break outTo suddenly happen without any warning.
4
EscalateTo become very big very quickly.
5
Fall outWhen two persons don't agree to each others' ideas.
6
DefendTo speak in favour of a person's side.
7
one thing led to anotherA series of things happening very quickly.
Reference:
National Council of Educational Research and Training (2006). Honeysuckle. The Quarrel (pp. 39-40). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.