Why is my 10k NTC thermistor on average accurate to 2C
Where is the "problem"?:

A problem is that you appear not to know (as there is not enough information provided) whether the error is from ADC on in or what the ADC 'sees'.  

Your problem may be in 


The thermistor accuracy (whether due to resistive heating or other causes) or 
In the conversion of thermistor resistance to indicated temperature or in 
The measurement of the voltages involved. 


Determining which one (or more) of these are problematic is an essential first step. Trying to fix errors in one area by 'playing' with another will never fix your problems.

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VOLTAGE MEASUREMENT CHECK:

A way of determining if the ADC reports the input that it should to within the accuracy expectable is better done by NOT invoking the Steinhart-Hart equation at all initially and working instead directly with voltage measured.  


Measure and report temperature of fluid before, during and after tests. 
Measure voltage at sensor with a suitable accuracy and quality DMM  
Measure sensor voltage with ADC.
Repeat with resistors 
Compare and report.


This allows you to know (and report) whether the actual ADC measurement is working correctly. 



NTC SELF HEATING ERRORS:

You report 11.858 KOhms at 20.82C.
Call that 12k for now.
Dissipation in the NTC = I^2 x R
I = 5V/(10k + 12k)
R = 12K
I^2 x R = (25/484.E6 x 12k ) 25/484/1000000
= 0.62 mW.  

Your thermistors datasheet specifies a dissipation constant of 1 mW/degree_C nominal.
So a 0.62 mW dissipation may be expected to give you about 0.62 C heating and a consequent shift in the apparent temperature.  

That's "nominal" with unstated assumptions by the manufacturer.  For example, varying fluid flow rate around the NTC will alter self heating effects. Encapsulating it will (probably) increase tem.

Adding "liquid electrical tape" insulation (while an understandable thing to do to achieve waterproofness" will probably have an unknown effect on the dissipation constant. 

In which direction does the error lie. The results given are ambiguous.
I'd EXPECT self heating to cause the NTC to report a HIGHER temperature than an accurate sensor does - is that what you appear to see? 

I could plug that potential error back into the equations, but it's something you need to look at and comment on. 



ADC RESOLUTION AND ACCURACY EFFECTS:

Your Arduino ADC has 10 bit resolution and maybe 10 bit accuracy.
With a 5V reference each bit has a resolution of 5v/(2^10) = 4.88 mV.  

At ~~21C / 12K the thermistor voltage will be
V = Vref x Rt/(10k+Rt)
= 5 x 12k/22k 
= 2727 mV.
A single ADC step as a %age of the reading is 4.88 mV/2727 
= 0.18% -> Say 0.2%.  

This is potentially far lower than the self heating effects.

A problem is that you appear not to know (as there is not enough information provided) whether the error is from ADC on in or what the ADC sees.  

A way of seeing if the ADC sees what it should to within the accuracy expectable is better done by NOT invoking the Steinhart-Hart equation at all initially and working with voltage measured.  


Measure voltage at sensor with suitable quality DMM
Measure and report temperature of fluid before and after tests. 
Measure sensor voltage with ADC.
Repeat with resistors 
Compare and report.


This allows you to know (and report) whether the actual ADC measurement is working correctly.

_____________________________________________________

Thermistor Dissipation Constant.

From here:
https://www.shibauraelectronics.com/products/technical/physical_03.html

"The thermal dissipation constant δ indicates the amount of power required for a thermistor to heat itself up by 1℃ when it is energized in still air (mW/℃).
When a power W is applied to the thermistor at an ambient temperature Ta and the temperature of the thermistor finally reaches a temperature T, the following equation is established.



Applying a power equivalent to the thermal dissipation constant makes a thermistor heat itself up by 1℃. This causes an error between the measured and the actual ambient temperatures.
Therefore, it is necessary to design circuitry to minimize the power to be applied so that measurement errors caused by thermistor’s self-heating are eliminated.
The thermal dissipation constant δ is determined by a balance between “self-heating” and “heat dissipation.” As a result, it varies substantially depending on the thermistor’s surroundings.
Placing materials that have a high thermal conductivity around the thermistor promotes heat release and increases the constant δ.
On the contrary, the construction allowing heat to accumulate decreases it.
Therefore, it is essential to select appropriate materials in assembling your thermistor.
It is also important, after assembling your thermistor, to measure the constant δ in its operation environment (air, water, oil, hot plate etc.) to see that the constant meets your requirement.