Why can't there be more than one method for determining New Moon Day?

Answer: To suggest that there is more than one correct method for determining New Moon Day is to suggest that Yahuwah's appointed times do not really matter, or are somehow negotiable.  This is an unacceptable proposition, as it irrefutably negates the plain commandments found in Scripture.

These are the feasts of Yahuwah, holy convocations which you shall proclaim at their appointed times. (See Leviticus 23:4.)

Scripture, here, plainly states that the holy days are to be declared in "their appointed times."  There is no room for negotiation.  Leviticus 23 goes on to list the specifics of Yahuwah's feasts, beginning with the Seventh-Day Sabbath.  There are specific dates and/or instructions given for each feast, the dates being reckoned according to the day of the New Moon.  For example, Passover is to be observed on the 14th day of the lunar month, counting from New Moon Day¹. 

To suggest that there is more than one correct way to reckon New Moon Day is to suggest that the specific day is not important.  Consequently, this implies that the timing of Yahuwah's feasts is not important, because the timing of every feast day (without exception) is dependent upon New Moon Day.  A lackadaisical attitude towards Heaven's Holy Days is unacceptable and cannot be harmonized with Scripture.  Yahuwah forbid that we should take lightly something upon which He has placed such great emphasis.

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¹ New Moon Day is the first day of each lunar month.