If each of you spend "even a $5 drink" each workday for a year, $5 per drink, x 52 weeks per year x 2 of you = $520.
If you want to use that $520 (or something less than that) on something else and it there are other things on which money is spent, possibly frivolously today, then the only way to identify that is by tracking it.
We don't know what your or his income is today. We don't know if you have combined your $ or if it is totally separate. We don't know how often each of you borrows from the other.
We don't know if you or he want to buy a car, a house, take a nice vacation somewhere, have outstanding debt (car, school, other loans) or even how old you and your boyfriend are.
Understanding your spending habits by tracking them is an easy way to know if money is being wasted or used efficiently. Everyone should have a budget - and step 1 is knowing where the income goes.
"But I know where it goes"... if so, then recording that to understand spending habits/trends can be very useful... Another method might be to set up a weekly "allowance" for each of you. My wife and I did this years ago. What's recorded is "allowance". Things we use jointly are not part of the allowance (i.e., gas, utilities, rent/mortgage, insurance, etc.) but things for individual consumption ("$5 beverage", lunch at work, beer after work with friends (not including SO), etc.)" must be managed within the allowance.
Our allowance amounts are not the same - but are reasonable enough to allow each person some flexibility. Base the amount on what is spent today. At the end of the week, if there is money left over, save it for treating yourself to something later. If it all gets spent before the week is over, your stuck - or use that which was saved earlier.
If he is entering his spending data, too, then I would not consider this "controlling". I would consider it "controlling" if he wanted you to enter your data only (and not his).
A little financial discipline now will reap later benefits as you get older.
Propose the "allowance"... another possibility is to propose putting a time limit on this record keeping... perhaps have a review of the recorded spending after 3 months. Both of you may have enough data to either continue or end the tracking.