Antonym of the given word

abet 

When you develop a product, you assess its performance for proper functioning.

Similarly, when you train a person to do a job, you analyze his/her performance to understand how good he/she is at it.

Hence, Develop : Assess :: Train : Analyze.

A bud is an undeveloped or embryonic shoot and may be specialized to develop flowers. Similarly, Seed is undeveloped and may be developed into a plant.

Hence, Flower : Bud :: Plant : Seed.

Given Pride is to lion as shoal is to ?.

Pride means a group of lions. Similarly, Shoal means a group of fish swimming. Here the other options have no relation with the given word in that manner.

Hence, Pride is to Lion as Shoal is to Fish.

Given Transition is to Change, and we know that Transition and change are Synonyms. Similarly, Immobility means not moving and synonym of immobility are motionlessness, stillness,...

Hence, Transition is to change as immobility is to stillness.

Here Pen is a tool which is used to write and poet uses it. Then, the needle is a tool which is used to stitch and it is used by Tailor. Except tailor, none of the other options is a person to use it.

Hence, Pen : Poet :: Needle : Tailor

Fumble means grope, mishandle, drop, mistake, blunder, bungle.

Finesse means skill, grace, elegance, assurance, diplomacy, discretion.

So, they are opposites.

Similarly,

Malign means slander or criticize.

Extol means being kind or good-natured. A person without finesse often fumbles. A person without extol in his heart often maligns.

Extol means praise or exalt, benevolence

Modern is used to refer to something new whereas antiquated is used with respect to something old.

In other words, both terms are the opposite of each other.

From the above analysis, the missing word should be a word that represents the opposite of weak. Strong is used to with great influence. Therefore, the apt word is strong or any synonym of strong like potent, powerful, keen,...

Hence, Modern : Antiquated :: Weak : Strong.

Here the relation between a fossil and extinction is that a fossil remains after an extinction. That is fossils are evidence of an extinction.

Similarly, puddle remains after it is rained. That is puddles are evidence of rain.

Therefore, Fossil is to Extinction as Puddle is to Rain.