Why is the 1uF capacitor needed in this load-sharing circuit?
Assuming you got the circuit from http://blog.zakkemble.co.uk/a-lithium-battery-charger-with-load-sharing/ you will note that the article specifically states that only 3 components need to be added to the basic charge circuit: Q1, D1, and R2. The article further states,


  C3 is an extra decoupling/bypass capacitor.


Since C3 is not necessary, it was presumably added as an afterthought, and the value was probably picked as a convenient number.