Because the transactions issued by clients are in principle executable in both branches.  Only a few transactions will be specific to only one branch: namely, those that involve coins that were mined in that branch, after the split.  

The incoming traffic is now ~120'000 transactions per day, on average.  For the last 12 months it has grown almost linearly at ~5000 tx/day per month.  If it continues growing at the same pace, by Jan/2016 it wil be ~150'000 tx/day.  The effective capacity of the bitcoin mining network, revealed in the recent stress tests, is ~200'000 tx/day or ~1400 tx/block.

Suppose that the miners split 90:10 between the 8 MB and the 1 MB branches.  The 8 MB branch will have ~130 blocks/day, which will have to carry ~1150 tx/block -- which is still less than the effective capacity ~1400 tx/block.  There may be "traffic jams" at peak hours or peak days, but the backlogs should clear after a few hours at most.

On the other hand, the 1 MB branch will have ~15 blocks per day only.  Each block would have to carry 10'000 tx, which is way over the capacity ~1400 tx/block.  So, every 10 minutes, on average, 1400 tx will be confirmed, and 8600 tx will be added to the queue.  The backlog will only begin to clear when the difficulty is readjusted and the block rate returns to ~10-15 min.  The adjustment happens every 2100 blocks, with is normally 2 weeks but in that chain will be 20 weeks.


Well, right now the 5 largest miners (who have ~70% of all hashpower) could cooperate to starve all the other miners, and take 100% of the block rewards intead of just 70%.  Or they could do much nastier things.