Given a 95% confidence interval why are we using 1.96 and not 1.64?

$1.96$ is used because the $95\%$ confidence interval has only $2.5\%$ on each side. The probability for a $z$ score below $-1.96$ is $2.5\%$, and similarly for a $z$ score above $+1.96$; added together this is $5\%$. $1.64$ would be correct for a $90\%$ confidence interval, as the two sides ($5\%$ each) add up to $10\%$.

To Find a critical value for a 90% confidence level.

Step 1: Subtract the confidence level from 100% to find the α level: 100% – 90% = 10%.

Step 2: Convert Step 1 to a decimal: 10% = 0.10.

Step 3: Divide Step 2 by 2 (this is called “α/2”). 0.10 = 0.05. This is the area in each tail.

Step 4: Subtract Step 3 from 1 (because we want the area in the middle, not the area in the tail): 1 – 0.05 = .95.

Step 5: Look up the area from Step in the z-table. The area is at z=1.645. This is your critical value for a confidence level of 90%.

http://www.statisticshowto.com/find-a-critical-value/

hope this helps