Why is Ibuprofen contraindicated in asthma patients?
Ibuprofen is an NSAID. So it acts by inhibiting COX (Cyclooxygenase) enzyme. What it signifies is that, if COX enzyme has been blocked, the PUFA (say arachidonic acid, here) will be converted to leukotrienes through lipoxygenase pathway.

Leukotrienes (LT) are of different types and have several target receptors; one of which is CysLT-receptors on bronchial smooth muscle. Once they are activated through LTD$_4$,E$_4$,C$_4$ , bronchospasm will occur. For asthma patients this is really fatal. So for them Ibuprofen is contraindicated.

Reference: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5072955/
Lo, P.C., Tsai, Y.T., Lin, S.K. and Lai, J.N., 2016. Risk of asthma exacerbation associated with nonsteroidal anti-inflammatory drugs in childhood asthma: a nationwide population-based cohort study in Taiwan. Medicine, 95(41).