Indicators for Strong Acid - Strong Base Titrations

When a strong acid is added to a strong base the products are water and a salt.
Water is neutral, that is [H⁺(aq)] = [OH^-(aq)]
 (or [H₃O⁺(aq)] = [OH^-(aq)] if you prefer)

The salt of a strong acid and base is made up of a cation that will not react with water to any appreciable extent, and an anion that will not react with water to any appreciable extent, so this salt does not affect the  [H⁺(aq)] and [OH^-(aq)] in the water, that is, the aqueous solution remains neutral.
At 25°C, K_w = [H⁺(aq)] × [OH^-(aq)] = 10^-14
Since [H⁺(aq)] = [OH^-(aq)]
K_w = [H⁺(aq)]² = 10^-14
√[H⁺(aq)]² = √10^-14
[H⁺(aq)] = 10^-7 mol L^-1
 So, at 25°C the pH of this salt solution will be pH = -log₁₀[H⁺(aq)] = -log₁₀[10^-7 ] = 7.0
A suitable indicator is one that changes colour at around pH = 7.00
Suitable indicators, for example, are bromothymol blue (colour change between 6.7 and 7.6) or phenol red (colour change between 6.8 and 8.4)

Phenolphthalein changes colour between pH 8.3 and 10. Phenolphthalein is NOT an appropriate indicator for a strong acid - strong base titration.

If we add a drop of phenolphthalein indicator to an aqueous solution of strong acid, the pH will be less than 7 and the solution will remain colourless. As we add strong base, hydrogen ions react with excess hydroxide ions to produce salt and water, so the pH increases. At pH = 7.0 all the strong acid will have been neutralised by the addition of strong base, BUT the phenolphthalein indicator will not have changed colour!
Phenolphthalein will not change colour until an excess of strong base (hydroxide ions) has been added and we have overshot the equivalence point for the reaction. The volume of strong base we record in this experiment will be too large!.

In strong base such as an aqueous solution of sodium hydroxide, the pH will be high and a drop of phenolphthalein indicator will turn the solution pink.
As we add a strong acid such hydrochloric acid, we will be consuming some of the hydroxide ions, and decreasing the pH. Somewhere between pH 8.3 and 10 we will decide that all our base has been neutralised by the acid because the indicator is now colourless instead of pink. But the reality will be that there is still excess hydroxide ions in solution waiting to be neutralised by the addition of more acid, so the volume of acid we have added, as indicated by the colour change of the indicator will be too low!

Learn all about how to choose an appropriate indicator for different types of acid-base titrations ar
https://www.ausetute.com.au/indicata.html