If transaction with small bitcoin is small transaction and the transaction with big bitcoin is large transaction. Then statement 1 is wrong.
They only have a finite amount of space in a block, so by including transactions paying the highest "rate" (not necessarily just a large total fee amount), they are more likely to receive the optimal payout for finding a block.
For arguments sake, if you only have 1,000,000 bytes of space... and you have 1 transaction that is 1,000,000 bytes and pays 0.01 BTC in fee... you think, that's a BIG fee... I'll use that one... well, the actual fee rate on that is 1,000,000 sats / 1,000,000 bytes = 1 sat/byte.
If you have 10 transactions of 100,000 bytes each paying 0.002 BTC in fees... then because their rate is 200,000 sats / 100,000 bytes = 2 sat/byte... you're better off taking the multiple "smaller" transactions with the larger rate. 10 X 0.002 = 0.02.
Outside of the logical choice being to maximise the amount of fees received, miners are essentially free to do whatever they like with regards to prioritising transactions... for instance, a miner could elect to ignore any transaction going to a specific address or group of addresses if they really wanted to... they'd be foolish to do so, because they'd be ignoring potential income, but they could do it.