I am doing this from memory as I don't currently have access to ArcMap, but I've done this task many times over the past 10+ years.
Create Upstream and Downstream Points:
Start by using the Feature Vertices To Points tool to make both upstream and downstream end-points for each pipe. You’ll find this tool in the Data Management toolbox under Features. Create them separately so you can join them to compare the diameters.
Spatially Join the Points:
Perform a spatial join between the upstream and downstream point layers you just created. This will allow you to see which upstream points are connected to which downstream points.
Compare Pipe Diameters:
With the spatially joined points, compare the diameters of the upstream and downstream pipes. You want to find the cases where the upstream diameter is larger than the downstream diameter.
Join Back to Your Pipes:
Once you’ve identified the points of interest, join the data back to your original pipe dataset. This will let you select the pipes where larger ones flow into smaller ones.
I would always check a handful of them manually to make sure you've found the correct pipes.
You can also automate this process using arcpy by replacing steps 2 and 3 with search cursors, making it much more efficient and quicker.