Why is budgeting regarded as both a science and an art?
Budgeting is first and foremost a science. Either the numbers balance or they don't. Producing a balance sheet that accurately reflects revenue in one column and expenditures in another column is a practice involving mathematical precision. Managers producing a budget spend considerable time and energy sitting down and calculating expected revenues and expenses for the coming fiscal quarter or year, which involves estimates based on sound judgement. If that involves "art," it is in the lack of precision that can reflect an economically turbulent period of time, anticipated disruptions due to labor problems, reduced productivity due to recapitalization of a factory, or predictions of inflation that may or may not prove accurate.
Listing anticipated expenditures is principally a matter of mathematical precision involving known costs, such as labor and materials. These costs can usually be known with a fair degree of accuracy, but, as noted above, anticipation of disruptions due to any particular development will complicate calculations. Predictions of inflation over a period of time, depending on the broader macroeconomic condition of the country, can be made reasonably accurate. An unpredictable event, like a terrorist attack at home or a war abroad, a natural disaster affecting a key part of the economy, or any other such incident can throw off the accuracy of a balance sheet enormously.
Expenditures can often be known with greater certainty than revenue, as market fluctuations, levels of competition, and other factors can either increase or decrease revenue during the course of the year.
Whether predictions or forecasts of economic performance can be considered "art" is questionable. As with meteorological forecasts, science is used to predict the outcome; intervening variables, however, can skew that outcome a lot, and imprecision can lead to bankrupties, of which hundreds of thousands occur every year across the country.