The answer a) is not 100% wrong but it requires such an unlikely context that b) is necessarily the expected one; c) is obviously plain wrong because of a gender mismatch.
Another reason why a) is wrong is that it is very rare in France for someone to drink a lot of tea for the breakfast ;-)
Here is the kind of context that would make a) acceptable :
Chaque matin, nous prenons beaucoup du thé que tu nous a offert. (see the ending note below)
As fierily discussed in other answers and comments, the expected form is:
Chaque matin, nous prenons beaucoup de thé.
The best French Grammar book, Le bon usage (§ 626, a), states:
La plupart des adverbes de degré employés comme déterminants indéfinis (assez, beaucoup, combien, moins, plus, trop, etc.) sont unis au nom par de dans le français régulier.
i.e.
Most adverbs of degree used as indefinite determiners (assez, beaucoup, combien, moins, plus, trop, etc.) are joined to the noun by de in regular French.
No explanation is given but a note states that in old French, these adverbs could also be followed by any of du, de la or des. Your question proves to be very legitimate: there is simply no obvious reason for de to be the current rule. You can't guess it, you have to know it.
In relaxed, regional or childish French, you might anyway ear:
(all examples from Le Bon Usage)
J'ai beaucoup d'l'argent dans ma poche.
Il y a beaucoup des gens qui...
On a quelquefois beaucoup du tourment dans notre métier (Alphone Daudet, Lettres de mon moulin)
Ceux qui ont énormément du talent (Charles Péguy, Esprit du système)
Ayant beaucoup des enfants, alors il se croit obligé d'aller en troisième (Raymond Queneau, Chiendent)
Note also that there are plenty of cases where beaucoup can be legitimately followed by du thé without breaking any rule.
- When it applies to a precise and determinate object:
Beaucoup du thé que nous buvons vient du Sri-Lanka.
- When the adverb beaucoup applies to the verb, not the object:
J'aimerais beaucoup du thé, s'il vous plait.
Cette infusion a un goût qui se rapproche beaucoup du thé.