why do some banknotes have 25 as their denomination?

ive seen old dutch banknotes and saw denominations of 25 and 250, i thought it was only the dutch until i saw haitian banknotes, with the same denomination too, and the aruban florin and the netherlands antillean guilder too, same for the cayman islands dollar, and the same case for mauritian and seychellois rupees and the south sudanese pounds as well, why is this the case?

Because it's a quarter of a hundred, or thousand respectively 🤷‍♂️

Canada also once issued $25 notes, the special occasion being another reason. There were also three issues of 25-cent notes in Canada earlier. 25-cent notes were also issued by the USA, akin to the denomination of the coins for which they helped supplement.

The reason is like what Idolenz mentioned.
Of the regular issues of Asia that I can think of:

Indonesia (former Dutch colony) : 2 ½ rupiah, 25 rupiah, 250 rupiah and 2500 rupiah banknotes
Burma : 25 kyat banknote
Singapore : 25 dollar banknote
India also : 2 ½ rupee banknote (George V was issued, George VI was prepared but never issued - the 2 Rupee was issued instead)
Of the commemorative issues Brunei and Singapore : 25 dollar notes, Nepal : 25 and 250 Rupee notes
Thailand : 2 ½ satang coins and 25 satang coins and I am sure many countries have similar denominations of coins issued

I am sure there are other many countries with such mid-denomination banknotes and coins
 

numisasia

The reason is like what Idolenz mentioned.
Of the regular issues of Asia that I can think of:

Indonesia (former Dutch colony) : 2 ½ rupiah, 25 rupiah, 250 rupiah and 2500 rupiah banknotes
Burma : 25 kyat banknote
Singapore : 25 dollar banknote
India also : 2 ½ rupee banknote (George V was issued, George VI was prepared but never issued - the 2 Rupee was issued instead)
Of the commemorative issues Brunei and Singapore : 25 dollar notes, Nepal : 25 and 250 Rupee notes
Thailand : 2 ½ satang coins and 25 satang coins and I am sure many countries have similar denominations of coins issued

I am sure there are other many countries with such mid-denomination banknotes and coins
 

but aren't some of these commemorative ones?? (except for indonesia)

Regular issues:

Burma 25 Kyat Pick 59 Banknote Book B1004 (other denominations in the series are 1, 5, 10, 50 and 100 Kyat)
India 2 ½ Rupees King George V 1917 Pick 2 Banknote Book B136 (also Burma Pick A6, but I consider it part of British India as it was issued prior to 1937)

Portuguese India 2 ½ Rupias 1917 issue Pick 22 Banknote Book B309 and Pick 22A Banknote Book 310, also 1924 issue Pick 24 Banknote Book B312
Singapore 25 Dollars Orchid Series Pick 4 Banknote Book B104 (other denominations in the series are 1, 5, 10, 50, 100, 500, 1000 and 10000 Dollar)

Commemorative issues (all to celebrate silver jubilee):

Brunei 25 Dollars Pick 21 Banknote Book B121

Nepal 25 Rupees Pick 41 Banknote Book B247, 250 Rupees Pick 42 Banknote Book B248

Singapore 25 Dollars Pick 33 Banknote Book BNP 107

Banknotes denominated in 25 Marks were also issued in Finland in the mid-1800s by one of the two issuing banks.

N#330461

N#330448

The reason for the issue of the 25 Mark notes was that the bank was prohibited from issuing notes denominated in 20 Marks. The bank also issued notes of 15 Marks, which were a substitute for 10 Marks which the bank was additionally prohibited from issuing.

Hibernia

Banknotes denominated in 25 Marks were also issued in Finland in the mid-1800s by one of the two issuing banks.

N#330461

N#330448

 

The reason for the issue of the 25 Mark notes was that the bank was prohibited from issuing notes denominated in 20 Marks. The bank also issued notes of 15 Marks, which were a substitute for 10 Marks which the bank was additionally prohibited from issuing.

why were they prohibited..?

pierregavin_09

 

why were they prohibited..?

An excellent question, I am glad you asked  it :)

Suomen Yhdyspankki (SYP)  (Union bank of Finland) was founded to support commercial activity on May 21, 1862. 
Initially, it did not have the right to issue banknotes, and  Suomen Pankki (SP) (The Bank of Finland) sought to prevent it from having the right to issue notes as it saw SYP as a competitor, and feared that SYP might abuse its right of note issue by issuing too many notes.

Shortly after its foundation, SYP proposed the issue of 25 Mk notes so as to not push any small notes of SP out of circulation, and thus not be a competitor to the State Bank. 50 Mk and 100 Mk notes were also proposed. In this era, several Swedish Private banks were issuing their own notes, establishing a precedent for private banks.

In January 1866 a decree was passed that authorised private banks in Finland to issue banknotes. SYP then decided to issue 1.5 million in notes, half the bank’s capital.

The bank petitioned the Emperor for the right to issue 5, 10, 25 and 100 mark denominations. SP were issuing denominations of 1, 3, 12 and 20 marks, and higher. After consideration, the Senate of Finland refused SYP the right to issue 5 and 10 Mk notes as they were considered to be in competition with SP small denominations. Instead, the Senate decided on 15 Mk as a replacement for the 5 and 10 Mk denominations.

Thus, SYP began to issue notes of 15, 25, and 100 Mk in April 1867, after Imperial approval.

Until 2013, The Gambia had banknotes for 25 Dalasis, but since 2014, 20 Dalasis notes have been released.

In 2011, South Sudan had a 25 Pounds note. Since 2015, a 20 Pounds has been released.

Aidan.

BCNumismatics

Until 2013, The Gambia had banknotes for 25 Dalasis, but since 2014, 20 Dalasis notes have been released.

 

In 2011, South Sudan had a 25 Pounds note. Since 2015, a 20 Pounds has been released.

 

Aidan.

Similar change in denomination has also occured in Portugal, although the other way around. When the 20 escudos banknote gave way to a coin in 1970's, the Banco de Portugal argued that the new coin should be 25 escudos instead, saying this denomination was more practical and many other countries used it. After 9 years of issuing new coins (1977–1986), the bank returned to the 20 escudos denomination again, arguing that the new 25 escudos was not very practical after all.  

A little unrelated

But in Burma their leader was told by a fortune teller he  would be rich if he made the currency in the country divisible by 9 …

”Ne Win also took drastic steps regarding the currency. In 1985, he issued a decree that 25, 35, and 75 kyat notes would cease to be legal tender, alleging that they were subject to hoarding by black-marketeers and were also used to finance the various insurgencies. Though limited compensation was offered, this wiped out people's savings overnight. At least one insurgency, that of the ethnic Kayan, was triggered by this act.^[57]

In 1987, reportedly on the recommendation of an astrologerthat the number nine was auspicious, Ne Win ordered the withdrawal of several large-denomination kyat notes while issuing new denominations of 45 and 90 kyats. Both 45 and 90 are divisible by nine, and their numerals add up to nine.”

 Not sure why they had a 35 bank note in the first place .

You have the 25EEK too ( Estonia )