1) you don't bleach cloth diapers that will ruin them (so bleach is not used for cloth diapers, but see below it is used for disposable diapers)
2) you don't use fabric softener on cloth diapers that will put a water resistant layer on so they don't work as well. (fabric softener is not used with cloth diapers)
3) when something goes to the dump it gets buried which delays the decomposition, paper can last for many decades even centuries,
4) liquid sewage can be treated water is a renewable resource, but once paper and plastic goes into the landfill those are not renewable, and there is only so much oil in the world and plastic is a oil based product
5) The energy used for washing is less then the energy used for producing one disposable diaper.
6) also ignoring that water is renewable, disposable diapers use more water in the production of them then in washing cloth diapers
7) disposable diapers use more chemicals then cloth diapers (they use bleach in disposable diapers)
8) more gas is used for disposable diapers they need to be delivered all the time, while with cloth does use coal (for the power plants) it produces a lot less CO2 the washer only runs for 35 to 40 minutes;
9) you can use the cloth diapers to save energy elsewhere and if like me you line dry there is no cost for drying the diaper, plus my line drying in my apartment means I don't have to run the humidifier, where I live I have a problem with the humidity dropping into the teens in my apartment but since I have been line during my diapers, I am able to keep it up into the 40% and even the 50% without using electricity to run the humidifier, plus using less water as the water used to rinse the diapers is the same water used to humidify my apartment, so now I am running the washer for up to 40 minutes every other day, instead of running the humidifier 24/7 so I can subtract from the energy usage of the washer the energy saved from not running the humidifier which I do need as when the air is to dry, in the 20%, I get nose bleeds so for health reasons I need higher humidity it not a comfort thing.doing some research I find a load of laundry will run about .13Kw, so per week that is, let's assume high load week 4 loads, .52 Kw, now the humidifier is about 67.5 Kw a day, now we take a look I need to run that 7 days a week *see links below for where I pulled numbers. True it does take 2 days to line dry but since I have 34 cloth diapers, and only use between 6 to 9 a day, I can let them dry for 2 days.
finally I don't do cloth for the environment but the cost. A nice stash of cloth diapers will run less than 1k, and if I was to do disposable I could run though that in about 5 months just for disposable ( I wear nearly all the time, the only time I don't wear is when at the office, and that is only 3 days a week, and 10 hours total counting drive and lunches) on my telework days and on weekend I wear all the time, and as soon as I get home on my office days I am right back into diapers. No the myth that cloth is just as bad or worse for the env has been debunked many times, there is only one study ever that showed cloth was worst for the env then disposable, and that was done by P&G (I sure they had an agenda there) This also takes into consideration the washing machine I use costs 1.75 per load (the dryer is another 1.75 but they are bad driers and usually takes 2 cycles to dry clothing, but as I noted above I line dry my diapers, and clothing) So my diapers and clothing run me about 7 a week, or 28 a month (note these washers are not in my apartment so I don't pay electricity or water on them, so that 28 is just the fee, and I don't have to pay anything extra a month for the washer). While disposables would run 100 a case, a case is only 40 diapers and I would need just over 4 cases of diapers a month (lets round down to 4, 40 diapers devided by my low number of diapers a day of 6 means a case would last 6 days, let's assume the week is only 6 days and we have an even number of only 4 weeks in a month, for only 24 days a month no more) that is 400 a month for disposables, and for 400 I can get a very good start on a good stash of diapers, so in 2.5 months I have a good stash of cloth diapers, also if you want you can add in an extra 4 a month for clothing detergent, that half of what a box costs me and a box lasts me about 2 to 3 months.
Also it nice to know I don't have to worry about running out of diapers, or have to wait for them to be delivered or fear they get delivered to the wrong apartment (UPS and FEDEX love to do that, they always deliver to the apartment below me my stuff)
*
http://www.bounceenergy.com/blog/2016/05/how-much-energy-does-this-appliance-use-humidifier/ (for hours per day, I do a load every other day, and it runs for about 30 to 40 minutes so I put .25 in for hours per day, I accepted the default wattage for the washer, but fill free to play with the numbers)
http://energyusecalculator.com/electricity_clotheswasher.htm (I used the TaoTronics TT-AH001: example but I am sure my humidifer used a higher amouth of wattage, then I had to take their number and muitiply by 2.5, as they used it for 10 hours and I have to run mine 24 hours if I don't line dry my cloth diapers)