As a slight aside – a good example of why you’d book 2 separate tickets is below. If you want to book Dubai to Brussels there aren’t any direct flights – and if you have a preference for Emirates (as many people do) then the below on one through ticket (which you’d want really with only 90 minute connections) is £2691.50 for economy.
EK 47 Y 15JUL DXBFRA HS1 1430 1920
LH 1024 Y 15JUL FRABRU HS1 2050 2145
LH 1005 Y 22JUL BRUFRA HS1 0830 0935
EK 44 Y 22JUL FRADXB HS1 1100 1915
Two separate tickets is £1013.40, so even if you got a slightly longer connection sorted in FRA the saving is huge. Why there should be such huge disparities in this day and age between the 2 costs seems strange to me. Obviously most people would book an alternative carrier – or maybe with a longer layover in FRA – but this does highlight why one would take 2 separate tickets and risk missed connections / none through checking of baggage etc.